The small hand had strayed as far as three when Reid took his leave of whoever was left in Edinburgh's Assembly Rooms, scene of an exuberant party to mark the international premiere of Sunshine On Leith, Dexter Fletcher's film of Stephen Greenhorn's play.
A hit when it was first staged in 2007, Sunshine On Leith threads the songs of The Proclaimers through a story involving the return to Edinburgh from Afghanistan of two Leith-born soldiers. Its screen version stars Peter Mullan and Jane Horrocks alongside newcomers George MacKay, Freya Mavor, Kevin Guthrie and Antonia Thomas.
At the premiere, Reid and his twin brother Craig were guests of honour, and joined Fletcher and the cast on stage to introduce the film. After its joyful closing number had brought lumps to throats and tears to eyes, they and the film won a standing ovation from the audience. Those who could still speak, cheered.
"I got a good vibe," says Reid when I ask him how it felt to see the film in its spiritual home after its triumphant screening at the Toronto International Film Festival. "It's the emotional reaction to it that counts, and the emotional reaction to it seemed very strong. That's what gives me hope that it's going to do quite well."
Although initially bemused that anyone would want to make a stage play based around their music, the brothers granted Stephen Greenhorn's request to use their songs and were delighted with the results. Audiences were too and the Dundee Rep production went on to tour nationally after its initial run. As a result the brothers had no worries about Dexter Fletcher's film version and took an equally hands-off approach. "The last thing we were going to do was look over someone's shoulder, criticise or offer an opinion before we'd seen anything - or even after," says Reid.
So how did he feel hearing his and twin brother Craig's songs in the mouths of others - sung in closes, pubs, hospitals, the streets and squares of the capital and, in the film's opening scene, in the back of a troop carrier in Afghanistan? "It's a very emotional thing," he says. "One of the most moving things for me was listening to the girls sing … whether you mean to or not, it changes something when a girl sings a song that was written by guys."
Over And Done With, slowed down and delivered as a series of drunken yarns in a raucous pub scene, is a case in point. And when nurse Yvonne (Antonia Thomas) delivers the line "This is a story about watching a man dying", it has a nuance that isn't present in its original version. Likewise, Make My Heart Fly becomes a yearning but playful duet when it's delivered in the stairway of a Leith tenement (though it clearly wasn't filmed in one: eagle-eyed locals have had fun pointing out the film's several Glasgow locations).
And as the film's title suggests, the pivotal moment comes with the singing of Sunshine On Leith. Along with the rousing I'm Gonna Be (500 Miles) it's the most popular song in the band's live set and its central themes - heartbreak, hope in the face of adversity, and how a love of place can soothe the first and inspire the second - have fixed it into the canon of Scottish folk favourites since its release in 1988.
"It's funny because in the end it's a love song, but it's turned from being a song from a man to a woman into something greater, or different," says Reid. "I don't know what it is that hooks people. But certainly the lyrics, which are devotional lyrics towards a woman but which then take on another meaning, must have something to do with it."
It's certainly a song that chimes with people - and not just supporters of Hibernian FC, who have adopted it as a terrace anthem. But although the recording of Sunshine On Leith will live long in Reid's memory - it was laid down in a studio in Oxfordshire the day England lost to Holland in the 1988 World Cup, with Dexy's Midnight Runners fiddler Steve Shaw performing the violin part - its beginnings were inauspicious. There was little inkling then of the power it would assume in the national consciousness.
"We'd been working on the song for a while and we had the melody but couldn't really nail it," Reid recalls. "Then we were flying into Edinburgh from London and, as it so often is, it was quite sunny over the Forth and you could see the city and the docks, and then Craig got it."
So, not inspired by the view from Calton Hill, then? No. Nor was the album's famous cover photograph shot there. "Most people think it is Calton Hill but it was right on the edge of the John Lewis building [part of the St James Centre at the top of Leith Walk]. That's where we got the best view for it so we were right up to the edge, frighteningly close to it."
The song didn't even make the Top 40, losing out by one place to a single from Page Three girl-turned-wannabe pop star Samantha Fox. But for Reid that's just another illustration of the slow-burn appeal of The Proclaimers' music. He has become used to songs assuming a life of their own after their release, acquiring adherents and then popping up in unusual places.
I'm Gonna Be (500 Miles), for example, may have given the brothers their only other bona fide hit after Letter From America, reaching number 11 in the UK charts. But in Australia it took top spot, and in the years since it has found favour in North America, being featured in several films. Actress Mary Stuart Masterson played it so much on the set of Benny And Joon it was included on the soundtrack. But it was its use in Shrek that really brought it to a new audience - and introduced the Anglophone world to the Scots word "haver".
"It's a bigger song now than it ever was when it was a hit," Reid laughs. "It's a perennial. There's acts who have had many more hits than us, sold millions more albums than us, who never have a record quite as enduring as that."
For Reid, that song's continuing success and the (fingers crossed) apparently universal appeal of Dexter Fletcher's film is part of a wider process which he refers to as "the normalisation of Scottish culture".
"When I was 15 and I heard Ian Dury singing the way he did, with a strong Essex accent and references to local things in east London or Essex, to me that was fantastic. I loved it. But it was very unusual to hear someone sing with a non-Americanised accent. So when we started off it was like a freak thing. Now you look at it and from Frightened Rabbit onwards every second band you hear sings with a local accent."
In his liner notes to The Proclaimers' 2002 Best Of compilation, long-time fan Matt Lucas writes that the Reid brothers write with "unabashed honesty and understated eloquence about what they know best - life, death, love, sex, marriage, parents, kids, football, politics, alcohol and Scotland".
It's quite a checklist, but unpack the songs and their meanings and those things are all there. "There are themes we keep coming back to, themes of identity, of a belief or lack of belief in a higher power - there's a constant battle between the two - and obviously love," says Reid. "I hope there's a reasonably good dose of humour in there as well. I think all that comes across in the film."
It's to Stephen Greenhorn and Dexter Fletcher's credit that it does - and to borrow again from the old country songs, amen to that.
Sunshine On Leith is released in cinemas on Friday