After some digging, I was able to find the full text of Brian McCleary's article in Fate magazine (May 1965 issue). I took screenshots of it and have included the imgur album on this post. You can read this for yourself for free on the Internet Archive.
According to Brian McCleary's Fate article, here is his story:
On March 24, 1962 Edward Brian McCleary, aged 16, was invited on a skin diving trip by his friend, Eric Ruyle, also aged 16. Skin diving just means diving without the use of a respirator; it's similar to freediving, though freediving is more of a competitive sport. Of note, Brian says he checked the weather report before agreeing to the trip. The two were joined by Bradford Rice, 14, Warren Felley, 16, and Larry Stuart Bill, 17.
They drove to Fort Pickens State Park, where they entered the waters of Pensacola Bay heading for the sunken USS Massachusetts, which is located on a sandbar about 2 miles offshore. The boys had a "seven-foot Air Force life raft," which they planned to paddle to the ship. It was outfitted with "a drift anchor, pockets for provisions, and oars." From the minute he sets foot in the water and continuing throughout the story, Brian stresses the fact that the water was ice cold.
The boys took turns paddling so no one would be too tired to dive once they reached the shipwreck, but on the trip out, a storm started to whip up. The sea grew choppier and clouds began to roll into the sky. The wind and waves were pushing the raft out to sea.
Eric, Warren, and Brian jumped into the water to push the raft from behind, but were unable to make any progress, so shortly after they climbed back in. The waves were so high that they now had to hold on to the sides of the raft.
The sky was growing darker, and other boats they saw out at sea began to head for shore. They saw a Chris Craft boat entering the channel. They waved at the boat, crying for help and shouting "mayday!" An elderly woman waved back, but the boat did not approach them to help.
Brad grabbed the shark gun, tied a red shirt around the tip, and fired it at the boat. The spear landed about 50 ft away from the boat. "It was impossible for anyone to miss the distress signal," but the Chris Craft continued on.
At this point, Brian spotted a large buoy and suggested they tie the boat there to wait out the storm. The crew, who are now sitting in a pool of cool water as they were continually swamped by the waves, paddled their raft towards the buoy. Brian describes the buoy was being twenty feet high. However, a riptide had formed at the base of the buoy, and the boat is sucked under it before the boys can tie the raft to it. Everyone jumps clear of the raft, which is pulled underneath the buoy, then washes free.
Eric and Brian cling to the sides of the raft as the rest of the boys climb back in. At this point, the sky is "black as night," and they are beginning to wash out of the channel past the USS Massachusetts.
After a while ("I don't know how long"), the storm lets up. The rain turns to mist and the ocean is calm, but a fog starts to roll in. It limits their visibility to 25 feet, and the boys decide to wait for the fog to clear. The boys share some cigarettes that miraculously hadn't gotten wet.
At this point, the water beneath them becomes unseasonably warm, and the air is filled with the smell of dead fish. They hear a splash and see:
what looked like a telephone pole. It was about ten feet high, with a bulb on top. It stood erect for a moment then bent in the middle and dove under. The sickening odor filled the air.
The boys discuss what this might be. Warren suggest an oarfish. Brian suggests a sea monster.
They then hear a "high-pitched whine." Panicked, everyone puts on their fins and dives into the water. "Patches of brown, crusty slime lay all over the surface." Everyone tries to swim for the shipwreck. The water begins to get colder and the rain rolls in again. I should stress that Brian has described everyone at this point being exhausted, cold, and cramped.
They have been swimming perhaps 30 seconds when Warren cries, "Hey! Help me! Help me! It's got Brad..." before he, too, vanishes. Brian is now swimming with Larry and Eric, but has lost sight of Warren and Brad.
Then, Larry vanishes. Eric and Brian dive for him, but see nothing. Eric becomes overcome with cramps, and holds on to Brian's neck as he paddles for what he hopes is the shore. It is now described as "pitch black," so he can't tell where he is going.
After what felt like a couple of hours, lightning flashes and Brian sees the USS Massachusetts. He swims toward it. Eric is pulled off him by a wave, but Brian sees him swimming towards the ship as well. But then:
Right next to Eric that telephone pole-like figure broke the water. I could see the long neck and two small eyes. The mouth opened and it bent over. It dove on top of Eric, dragging him under. I screamed and began to swim past the ship. My insides were shaking uncontrollably.
At this point, Brian does not remember anything until he washes up on a beach. He finds "a tower of some sort," which he climbs and sleeps on the floor. In the morning he climbs down, but his legs fail him and he falls to the beach and starts to crawl, where some passers-by find him.
Here is the sketch of what Brian McCleary saw.
The article published in Fate ends with a short summary of local news reports, which don't match all of Brian's story:
One report says Brian 'drfited and swam more than two miles' but Coast Guard and Navy rescue units estimated he swam five miles. Doctors at the Naval Base said he was in the water over twelve hours.
The interviewing reporters told Brian their stories would not mention the sea serpent as it was "better left unmentioned for all concerned."
The bodies of Eric Ruyle, Warren Sullay, and Larry Stuart Bill were never recovered. One body washed ashore a week after the accident and Brian says, "To the best of my knowledge, I identified the body as that of Brad Rice."
I was unable to find confirmation of whether or not this was Brad Rice or why Brian was the one to identify the body.
The raft was found ten miles from where Brian came out of the water. He was picked up near Fort McRae about 7:45am Sunday, March 5, 1962, by a helicopter from the Naval Air Station He had spent the early morning hours in an old gun emplacement.
The clipping further states Brian was suffering from shock and exposure but was released to his parents after brief treatment in the Naval hospital.
Brian writes us that after the accident he had a nervous breakdown but recovered and was able to resume his life in about three months.
This newspaper article from the Ocala Star-Banner confirms that the four boys were lost at sea, and Brian's story of attempting to tie the raft to a buoy. The raft eventually washed ashore on Gulf Beach, with face masks, shoes, and fins still inside. (Remember that the raft did have pockets to stow things in, so it is possible for these to have remained inside, and the cigarettes to have remained dry if stowed properly.)
Location
I tried to sort this out using Google Maps. The boys go to Fort Pickens State Park- easy enough to find. See map here.
Brian describes climbing "three stories of the main embattlement, a long rectangular structure with a square brick tower on top of which is mounted a telescope," through which he looks and locates the ship. They then climb down and launch their raft on the beach.
The battery closest to the USS Massachusetts appears to be Battery Cooper, pictured here.
However, Brian does describe the "channel," which appears to be between the keys of Fort Pickens and Fort McRee, so they may have launched farther from the wreck.
The Weather Problem
Other write-ups claim that weather reports do not mention this storm. I was unable to confirm this with my own research (I did find this which says there was no rain but doesn't provide much detail.
I was unable to load this tool. The zip code for Ft Pickens is 32561.
I don't know if other Pensacola residents who may have been boating that day were interviewed. Minor squalls can blow up on the sea pretty frequently, so this isn't a deal-breaker for me; the ocean is very changeable, as is its weather.
I did not check the high/low tide reports, however the boys were clearly out overnight so the tide would have been changing at some point either way.
It was a Rip Tide/Rip Current
This looks like the most likely answer. Here is the Wikipedia article on rip currents.
Here is an actual picture of multiple rip currents on Pensacola Beach.
So they're definitely in the area, though the boys were a ways offshore.
Given that they were in what is described as a "channel," particularly knowing that the USS Massachusetts is on a sand bar, it seems likely that a rip current could form there. I do not know the specifics on how rip tides form, though, or if they could form 2 miles offshore. However, looking at the map of Battery Cooper, this does look possible. You can clearly see a deep channel between the shallower keys that sweeps out to sea.
The Boy's Mental State
It is repeatedly stressed throughout the article that the water is freezing, the boys are physically exhausted, and are cramping pretty badly. It is entirely possible that the "monster" was just a hallucination, and the boys drowned as they tried to swim back to shore after panicking at being swept out to the ocean. Anecdotally, anyone who was experienced paddling against the tide (I certainly have) can attest that it is very difficult and tiring. In any event, given the described state of the boys, it is not hard to picture how they drowned, regardless of what sequence of events led them to that point.
So was there even a sea monster?
Well, maybe.
The Whale Theory
This comment claims that the sighting of the "sea monster" may be a North Atlantic whale skim-feeding. Check out this photo, which looks pretty damn similar to a plesiosaurus.
You may also view this video which shows a whale filter-feeding, eerily similar to what Brian describes.
Quite frankly, just seeing this video and knowing it's a whale freaks me out, let alone if I was in the ocean with this creature.
While baleen whales do not eat humans, obviously, it is not directly stated that the monster ever eats anyone. The boys are panicked at the sight, and start frantically swimming away; they are already exhausted and cramping, and could easily drown in their attempt to escape from the "monster." The "monster" does not eat Eric, either; it "dives on top of him," dragging him underneath. A whale is a massive creature and could easily hurt a human. While whales will generally try to avoid humans, it's possible that they could accidentally dive on top of one while feeding if they didn't know it was there. A whale could also pull a person down as they dive if the person is close enough, and in their weakened state, the boys could have drowned.
Other evidence to support this is the "high-pitched whine," which I feel is kind of self-explanatory - that's a sound a whale makes. The mist could be a whale spouting, and the scent of dead fish would make sense as well (I have never been that close to the mouth of a whale, but I can't imagine it smells pleasant).
This article describes an injury by a baleen whale; this one refers to a series of injuries caused by swimming with whales.
This is the theory I favor - I think the boys were caught in a rip tide, saw a whale, panicked, and drowned.
But then what was the "telephone pole"?
I have no idea. What do you think?
Did Brian kill them?
This seems unlikely to me. It sounds like Brian was extremely traumatized by this experience and while survivor's guilt could be a part of that, I really don't see him causing the death of his 4 friends. Some people say he paddled the raft away from his friends as a joke, causing them to drown, but I think that their accidentally drowning while being caught in a rip tide is more likely.
It was a vicious grouper.
I have dived with groupers before, and while they are HUGE, they are pretty chill fish and they don't look anything like this described sea monster. Here is what a grouper looks like.
Here is a grouper "attack". They're not going to pay any attention to you if you don't have a fish for them to eat.
Fate Magazine is a tabloid and this is all made up.
Well yeah, maybe, but that's no fun, is it?
This article, from a clearly reputable source rains on our entire parade, though it offers some evidence that something happened:
[T]he Pensacola News Journal quoted McCleary at length on 26 March 1962, including this description of the fatal incident:
“Larry, Eric and I tried to swim together. Eric suddenly developed cramps. Larry and I tried to hold him up and suddenly my legs stiffened and I wasn’t able to use them to swim with. I tried to get Eric to hold onto me. He finally started shouting that he couldn’t make it. I told Larry that I didn’t think we were going to make it and he said, ‘We’re sure going to try.'”
Whatever happened next remained unstated, as McCleary jumped ahead to his arrival on the shoreline, by himself. There was no mention of a monster, or indeed any description of what befell his friends. More to the point, the Playground News of 2 April 1962 reports the funeral of Brad Rice, washed ashore on 31 March, a presumed drowning victim. Larry Bill, Eric Ruyle and Warren Salley Jr. rated no mention at all.
The article goes on to consult the Social Security Death Index and claims that the latter 3 did not exist at all.
Here is Bradford Rice's grave, which matches this story and includes a newspaper article.
However, I, a random Reddit author and much more reputable source, say that's no fun and we should continue to wildly speculate anyway.
What happened to Brian?
I have read posts that claim that Brian went on to abuse drugs and insist that the sea monster existed, and also posts that say Brian say a psychologist who convinced him that the monster was not real. There are no sources to confirm either way.
Edward McCleary died in 2016. Here is a link to his memorial page. Here is another. Please be respectful and do not contact or harrass any of his friends or family.