The 45-year-old former Cowdenbeath manager now enjoys a less pressurised existence as technical director of the Braddock Road youth club in Fairfax, Virginia, but it takes little prompting for his thoughts to return to May 16, 1996, when he helped Dundee United become the only side actually to be promoted to date via a play-off between the top two divisions.
Amid chaotic scenes at a sold-out Tannadice Park, with one last flick of that trademark ginger middle parting, Welsh sent in the towering last minute header against Partick Thistle which cancelled out an Ian Cameron penalty to bring the aggregate level at 2-2, laying the foundations for the breathless extra time period which saw Owen Coyle's winner seal promotion. United have resided in Scotland's top division ever since, but Welsh's play-off claim to fame doesn't end there. Having been transferred to Hibs shortly afterwards, there he was, back reliving the ordeal in the colours of the Easter Road club 12 months later, as they secured their survival against Airdrieonians by a 5-2 aggregate margin. How Hibs, despite a 2-0 advantage from the first leg, would take a similar result against Hamilton this afternoon.
"I played in back-to-back play-offs, in fact I am probably the only man in history to do so," Welsh told the Sunday Herald. "I enjoyed them because they are big games, but they are certainly a bit nervy. They did away with them but I don't think they should have done. It was great excitement and drama for everyone."
As it turns out, Welsh's enjoyment of the Partick Thistle game is rather spoiled by the audio.
"I have watched that goal a couple of times, and the commentator says 'for once Brian Welsh puts it in the net'," recalled the rugged central defender. "I always think 'you cheeky b*****d, you have just spoiled that goal for me forever'.
"But I was pumped up and I remember after scoring that goal, with the confidence we had, there was only going to be one winner," he added. "At the end of normal time, I couldn't stand still, there was so much adrenalin flowing. I think everybody knew we were going to win it and that was the way it turned out. It was a packed stadium, a great atmosphere. Andy McLaren did brilliantly that night, setting up the goal- he did magnificently. But I look back now and the players that came through for Dundee United around that time were absolutely frightening. In my reserve team we had Billy McKinlay, Duncan Ferguson, Ray McKinnon, John O'Neil, Andy McClaren, myself and Allan Preston. It was an unbelievable group.
"Having said all that, that night was the last game I played for Dundee United. I signed for Hibs that summer and we ended up in a play-off against Airdrie. We went down to 10 men and the first game was nervy, but we still won 1-0 at Easter Road, with big Yogi [John Hughes] scoring, and in the second game we ended up winning 4-2. It became quite comfortable."
As successful as his dalliance with the play-offs was, far less comfortable was the fact that Welsh did have the unfortunate distinction of participating in relegation seasons at both United and Hibs.
The chance of some prior late season goalscoring heroics with United in 1995 was ended when he was serving a four-match suspension while a resurgent Aberdeen side condemned them to relegation by claiming the play-off place at their expense, while he was also injured when the Easter Road club were relegated in 1999.
"To get relegated with Hibs was horrible, just absolutely horrible," said Welsh. "I remember the last game, it wasn't nice. At the time Hibs had a lot of foreign players and I thought a lot of them were laughing their heads off at the end.
"Hibs are on a bit of bad run right now and that is a worry," he added. "In the play-offs you have to be playing well. If you are a team that is on a downer it is not easy to pick yourself up. People always look to the second game but I think the first game is very important. If I remember rightly with United we could have put that one away in the first game against Thistle. We didn't, and that is why we ended up very nervous in the second game."
Welsh keeps loosely abreast of developments in Scottish football, but his focus now lies elsewhere. He oversees 500 kids at the Braddock Road youth club, where David Bagan, once a cup winner at Kilmarnock, and Welsh's own son Michael are also coaches, and recently used his contacts to send one of his most promising players over to Chelsea for a week's training.
"I have been out here for two-and-a-half years and I have been home once in that time - so that kind of tells the story," he says.