Brazil is a skilled raconteur and it's a laugh a minute when we chat over the phone. It is easy to see just why May thought he would be the perfect fit into this eclectic group of supremely skilled players.
In many ways, it was the cobbled-together nature of this iconic squad which is why fans took to them so much, Brazil says.
"There were a lot of rag-tag players who weren't wanted by their clubs," the former centre back remembers.
"The youngsters he brought through, Jason Perry, Blakey, Damon Searle, Lee Baddeley, he brought through players he thought were good enough to win the league.
"Couple that with myself from Man United, Daley from Chester, Nicky Richardson from Halifax, Stanty who had been all over the place, Kevin Ratcliffe who people thought his legs were gone.
"Eddie got the best out of us all.
"If you think about Eddie, a lot of people thought he was just a manager. He wasn't.
"He was like a father, a best mate, a confidant, a psychiatrist. He was everything.
"If Eddie was alive today, God bless him, and this was his era, he would be one of the top managers."
Brazil laughs when he thinks about an occasion when Stant threw his shirt at kitman Harry Parsons when he was substituted in one match.
They were drawing at the time and went on to win, but in the dressing room May and star striker Stant squared up after the manager had gone ballistic.
"I wouldn't have fancied Stanty's chances if I'm honest!," he laughs.
There are many memorable moments which stick out in Brazil's mind, some special, some not so much.
He loved the Ninian Park crowd and cites the tremendous bond which seemed to unify the players and those paying to come and watch them every Saturday afternoon.
"If we weren't doing well, you'd hear the odd heckle from the stand," he says. "But you'd look up and realise you'd met him on the Wednesday night at the Wine Press. So you couldn't let him down!"
City were on a magical run towards the end of that season and it was the penultimate game against Shrewsbury at home, a game which the Bluebirds needed to win to seal promotion, which evokes more laughter from the effervescent Brazil.
"Before that game, all the boys said we should all have a skinhead, I've gone, 'Yeah, I'm up for that!'," he recalls.
"I end up getting a skinhead, did anyone else? No. I just end up looking like Vinnie Jones!"
Of course, City won the final game, too, and were promoted as champions. An amazing feat and one which Brazil believes justified his move down from Old Trafford down to Ninian Park.
He had more enjoyable years in the Welsh capital and was becoming part of the fabric, but his fortunes changed when Phil Neal and Kenny Hibbitt took charge and injuries began to take its toll.
By 1996, then still just 27, Brazil could feel his time was coming to an end and it's clearly a time which still evokes strong memories within him.
"It was pretty sad when I left," he remembers. "I kind of knew. I had missed the last two or three months with a bad hamstring tear.
"I wasn't a big fan of Phil Neal or Kenny Hibbit. I had my best years under Eddie, so I was kind of biased.
"I went in and knew they were going to release me.
"Phil Neal says, 'Look, you've been a great servant for the club.'
"I said, 'Can I just stop you there? If you're going to offer me a two-year contract, I'm refusing it!'
"His face just dropped. They had no intention of offering me anything!
"I said, 'Look, I've been at this club a long time now and I think you two are taking this club the wrong route, you're taking it down. So I want to leave.'
"Phil Neal was trying to get his words out but I just wouldn't let him say it!
"I thanked Kenny and told them I had an appointment and had to leave, I was meeting the boys in the Admiral Napier, I had to get a shift on!
"I walked out the door into the small car park and literally had tears in my eyes. Just sadness. In the four years I was there, the club and the fans meant so much to me.
"I was in tears in the walk from Ninian Park to Canton."
Once again, he had offers to leave for China or to return back home to Ireland, but he had built an affiliation with South Wales and managed a move to Newport, part-time while he did his coaching badges.
It turned out to be an important move. He has his own business now whereby he goes into schools to teach PE and sports lessons.
Brazil had stints as a football development officer for both Newport and Cardiff City and, of course, went into management with the likes of Haverfordwest, Goytre United and Pontypridd Town.
"Thank God for Newport," he says in hindsight. The opportunity to do those coaching badges there has given him his livelihood for more than 20 years now.
He has also dedicated much of his time post-football to helping the homeless. He has close ties with Huggard, a centre which helps rough sleepers in Cardiff.
Brazil, who now lives in Penarth with his girlfriend and his nine-year-old daughter, Ava, launched a shoebox campaign last winter and spend Christmas Day handing out supplies to the homeless in the capital.
He works in schools Monday through to Wednesday and does his volunteer work on Thursday and Friday and enjoys it all. He loves giving back, be it through sport or helping the homeless.
Recently he has branched out into after-dinner speaking, too, and after one phone call you get the sense he will do alright for himself in that industry.
He also still works for Cardiff City, on match days as an ambassador. In fact, it is in this line of work where he encountered the most astonishing tale of them all, with his former boss Sir Alex Ferguson.
"I met him six years ago, when Cardiff first got into the Premier League and Manchester United came down to play," Brazil recalls.
"Ferguson was in the directors' lounge and Keith Cooper told me he was in there. I went in there and there he is, suited up, and I hadn't seen him in about 15 years. Bobby Charlton was on the table, the directors etc.
"As soon as he saw me, he stood up and said, 'Baz, sit down!' He asked me how I was doing and all that and then he started going on about Roy Keane, who had a book out at the time.
"'He's doing my head in at the moment,' he said about Keane. So I was just laughing.
"But he said, 'Anyway, how are Mick and Evelyn getting on?' My parents! Lucky I was sitting down. And I thought that was a shock in itself, given I'd not seen him for 15 years.
"But then he turned around and said, 'Is your dad still driving a taxi?'
"I already respected him, but when I came away from that... I could understand him remembering Bryan Robson, Norman Whiteside or Peter Schmeichel's family, but for him to go into that level of detail, to know everything about you and your family.
"I don't even remember some people I worked with two weeks ago! That just shows why he's been such a top manager for so long."
It was Ferguson, remember, who thought Cardiff would be the perfect fit for Brazil, and so it turned out to be.
So, standing there in Ferguson's office 27 years ago, does he think he made the right decision?
"I've made a lot of wrong decisions in my life," he says. "That's definitely got to be up there with the top ones I got right.
"I love Cardiff. I've watched it change. In those 27 years, I've seen the stadium change, managers come and go, how they've built it all up.
"One thing that has never changed has been the fans. They are always so true, so loyal to the club whichever manager is there.
"To this day, they are still amazing, there's no one like them.
"They are the heartbeat of the club in so many ways, the club wouldn't survive without them."
Former Cardiff City player Derek Brazil with his old Manchester United boss Sir Alex Ferguson
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