The 39-year-old Alexander stayed and has steered Ilkeston into contention for promotion from the Midland Division of the Dr Martens League. They are also in the second round of the FA Cup for the first time in 50 years of entering. Second Division Scunthorpe, away, bar their way to a brush with the big time on Saturday.
While their supporters dream of beating nearby Derby or Nottingham Forest, or a day out at Old Trafford or Highbury, Alexander has warned his players to focus on the task in hand. "I've told them: if you win, you'll get a crap draw, whereas if you lose, the team who beat you will get Manchester United."
This sub-clause of sod's law could be from the Barry Fry book of folk wisdom, unsurprising given that Alexander played in his attack when Barnet were in the Vauxhall Conference. "I'm probably one of the few people who thought Barry wasn't too bad tactically," he said. "He bought the best players, so the tactics and team picked themselves. Training was always fun and I enjoyed playing for him.
"I also have him to thank for breaking into League football at 28 when he sold me to Alan Buckley at Grimsby. I picked up some man-management skills from Barry, but Alan's the man I learned most from."
Alexander's chance to put his theories into practice came four years ago at Lincoln. As youth coach he had been instrumental in honing the skills of Darren Huckerby and Matt Carbon, now with Coventry and Derby respectively, but his elevation to the managership was short-lived. "The chairman said: 'Give it 12 months and we'll see how it goes'. We started well, then fell away a bit. He sacked me." The fact that he was the League's first black manager, just ahead of Viv Anderson at Barnsley, was "neither here nor there". Supporters and directors were, he believed, concerned solely with results.
Alexander returned to working with young players at Mansfield. Two years ago next February, by which time he had become No 2 to Andy King, he was asked whether he wanted the job left by Leighton James' demise at Ilkeston. The team were beyond salvation, having lost 17 of the previous 19 games; the club's potential made it an offer he could not refuse. They had recently moved to a new site and in the chairman, Paul Millership, they had a benefactor with a seven-year plan to reach the Football League. Alexander now has 10 YTS boys - unusual for a club of Ilkeston's status - and players, having heard of their reputation for paying well, ring him to offer their services.
The spine of the side has been rebuilt to telling effect. In goal, Malcolm Rigby was once bought by Forest from Notts County and, at 21, is starting to fulfil his promise. The captain, Nicky Law, brings the experience of some 539 League appearances to central defence. Up front, ex-soldier Matt Carmichael scored both goals in the first-round defeat of Boston United (Ilkeston's sixth tie in a run dating back to August) and faces one of his former clubs on Saturday. "I had Matt at Lincoln and sold him to Scunthorpe," Alexander said, adding humbly: "Not one of my better decisions."
Carmichael was signed to replace Simon Grayson, who now plays before far bigger crowds as a trumpeter in Sheffield Wednesday's brass ensemble. Alexander's part-time band hope to call the tune at Glanford Park, but their manager knows he could yet end up facing the music from those impatient fans.
"I expect to be back in the League one way or another," he said, blowing his own trumpet, "but if we don't go up, the Cup will soon be forgotten and people will say: 'He's had his two years, it's time for him to go'."