Appointed in the hope that he would match the success that Graeme Souness enjoyed at Rangers, Brady found himself at a club in turmoil. A dynasty was fighting to retain power in the boardroom and his players were not up to standard on the pitch. Across the city, Rangers' financial resources dwarfed those Brady could call upon. The few big signings that he did make did not bring success. Last October, drained and defeated, Brady left.
It was his first managerial role and Brady, financially independent and widely respected, could easily have decided he could do without the hassle. The cosy world of media punditry beckoned.
But there he was on Wednesday, a year to the week after leaving Parkhead, celebrating on the touchline as his Brighton and Hove Albion side knocked Leicester City out of the Coca-Cola Cup.
It was an impressive result, especially as his Second Division team beat their Premiership opponents in both legs. It also illustrated the extent of the club's progress under the former Irish international midfield player.
Only 11 years ago Brighton were in the old First Division and reached the FA Cup final. Yet when Brady took over last December the club were two from bottom of the Second Division and in danger of going into the League's basement for the first time in 30 years. That was the optimistic view. The pessimistic one was that they would go out of business altogether.
It took the financial intervention of the new chairman, Greg Stanley, to stave off a High Court winding- up order and ensure there was a club for Brady to manage. Brady then set about saving the team.
'The morale of the club had almost disappeared,' Brady said yesterday. 'There was a sense of apathy and resignation about it. It had got to everybody - supporters, staff, players.
'One of the things I tried to do was impart a sense of belief, but you can only get that across if you start to get a few results. Luckily enough, in the second game we got a home win. Then we went to Plymouth, who were second in the table, and got a draw. The whole thing went from there.'
The supporters, who had expected the departing Barry Lloyd to be replaced as manager from within or by a former Brighton stalwart, had already reacted positively to Brady's appointment. His first home match in charge attracted the first crowd over 6,000 that season. The second brought the biggest League gate for 18 months. By the end of the season, after a late run pushed them into play-off contention, there were 15,000. Together the supporters, Brady and the team have created that most important and elusive of moods in football - confidence.
The support had been attracted by Brady's name, which, he agrees, also helps with the recruitment of players. However, he adds: 'It works initially, but your reputation does not count for much if you don't know your stuff.'
Brady brought in a former Brighton player, his one-time Republic of Ireland team-mate Gerry Ryan, as coach; Jimmy Case, the former Liverpool midfield player, was brought back from Sittingbourne; and Mark Flatts and Paul Dickov arrived on loan from Arsenal.
'We got a bit of organisation in the side,' Brady said. 'When morale goes the will to work goes. We brought that back. We gave the players guidelines as to what was expected and I think they appreciated that. They needed someone to tell them what to do and what not to do and they responded.
'Bringing Jimmy in was a good move. He has so much presence. Despite his age (at 40 he is the oldest outfield player in the League) he is still a very fine player in this standard of football. I ask him if he is up to it: if he says 'yes' he is in the team, if he says 'no' he has a rest.
'I have never played at this level myself, but that is not a problem. You have to expect players to be capable of a little less, but that's all. It is the same game.'
The Brighton job was the first Brady had applied for after leaving Celtic. 'I needed a couple of months' rest after that,' he said.
When he was offered the chance to join Brighton it was not a case of needing a job but wanting it. Like Kevin Keegan at Newcastle and Glenn Hoddle at Chelsea, Brady is one of the new breed of managers with the financial security to manage the way they want to.
'I don't think any chairman - well certainly not here - would tell you to change the style of play, but some attempt to push players upon you and try things. Independence means being able to say: 'No, I'm not going to do that'.'
That independence became treasured at Celtic, where the off- field wrangles inevitably handicapped Brady's efforts.
'The main problems there were nothing to do with football,' he said. 'Few clubs can maintain playing standards at times of instability. With the club in turmoil, every game was a do-or-die game and being new I found it difficult to relieve the pressure on players, which is very important.
'I know now what 'pressure' means. When results go badly I will be better equipped to cope. I will know how to handle big games when there is a lot at stake. I had my chance. There are a few things I regret. I don't want to go into them, but I won't make the same mistakes again.'
He made few as a player. Having started as a youngster with Arsenal, Brady went on to play for four Italian clubs before returning for a curtain call with West Ham.
It was an appropriate end, for Upton Park was a natural arena for Brady's refined gifts. He was a rare artist in a League dominated by grafters and harriers and it had been a considerable loss when he went to Italy in 1980.
Even though the Premier League has since changed dramatically, he believes he would make the same decision today.
'Our game is more attractive and focused, but it is still not as big as Italy. Italian football is on a down at the moment. The country is going through a dramatic change and it is having an effect on football. There is not the same enthusiasm about the game.
'But you still pick up the tabloids and see that Shearer's supposed to be off to Milan, or Giggs to Juventus. Why's that? The money is the main thing, but it is not the only one.
'I wanted to go anyway. I had seen how well Kevin Keegan had done abroad and that gave me the ambition to go and try. Arsenal were lacking in ambition at the time.'
Brighton play football the way Brady liked to play it. 'I'm not keen on the percentage game, lumping it forward as a hit-and- hope,' Brady said. 'We don't have a big man in attack. I want players to be constructive.'
Brady has brought in two players from Tottenham who follow that philosophy, Jeff Minton and Junior McDougald. The latter - 'a footballer, a positive, exciting dribbler' - partners the coveted Kurt Nogan in an attack that is especially dangerous on the break.
Brighton's reward for beating Leicester in the Coca-Cola Cup is a home draw against Swindon. 'It would be nice to go to Highbury or Old Trafford, but we'll try and make that the next round,' Brady said. 'We all feel we have a chance to get through.'
The League remains the priority, however, and today 11th-placed Brighton visit sixth-placed Bradford, who were Brady's first opponents at the Goldstone Ground. 'If we can maintain a promotion challenge I'll be very happy,' he said.
And then? The man himself will not countenance suggestions that his long-term aim might be to follow George Graham through Highbury's marble halls, or to lead the Republic of Ireland.
'My ambition is solely here,' he said. 'There is a lot of potential. Realising that would be success for me. Brighton and Hove Albion should be at least in the division above and they should be knocking on the door of the Premier.
'Once we give the club a Premier look - and the proposed move to a new stadium should help - that is the aim. There is a big catchment area and we want the people of Sussex to sit up and think: 'Something's happening here'.'
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