As McCoy sips on a gin, fellow cast member Finn Den Hertog is expounding on something which appears small from the outside, but once inside is infinitely more expansive.
"Now, where have I heard that before?" deadpans McCoy before picking up his gin and his walking stick en route to the theatre's boardroom, which for some reason has had its full-length table removed. The effect, while no Tardis, makes its space seem far larger than it actually is. McCoy's wry little in-joke may refer to how a certain generation of science-fiction geeks know him best for his 1980s stint as Dr Who, but as his role in Plume proves, there's been a working life since playing the iconic Timelord, and there was certainly one before it.
While he's just spent the best part of two years in New Zealand filming Peter Jackson's latest big-screen Tolkien adaptation, The Hobbit, McCoy's earliest screen appearance was on the educational show for hearing-impaired children, Vision On, before graduating to Jigsaw and Tiswas. In the midst of all this, the artist formerly known as Percy James Patrick Kent-Smith was putting ferrets down his trousers alongside the likes of Bob Hoskins in anarchic 1970s fringe theatre troupe, The Ken Campbell Roadshow.
"Some people are maybe a bit surprised when they see me in something like this play," he says. "In (TV sitcom) Still Game I played a rather sad character, who comes out after 40 years of locking himself away in his tenement, sees the new Glasgow and decides he doesn't like it so goes back in and locks the door again. Then in Rab C Nesbitt I played Rab's lunatic brother who escapes from the asylum, and again that was quite a tragic character. Most of the other work I've done isn't like that. Not in England, anyway, where they don't seem to see me like that, but in Scotland it's different. I didn't get cast up here at all for a long time, and then I played a character on TV called Angus, and that's when people up here realised I was a Scot."
At the Edinburgh International Festival, McCoy actually played Scotland in John McGrath's late period spectacle, A Satire of the Four Estates. Also at EIF, he appeared in Jo Clifford's version of Calderon's Life is A Dream, and in The Hypochondriack at Edinburgh's Royal Lyceum Theatre. More recently, McCoy appeared in post Sanjeev Kohli's cornershop-set BBC Radio 4 vehicle, Fags, Mags and Bags. Plume is something else again.
"It's a beautifully written play," McCoy says, "about loss and sadness, and the change in a human being because of that loss. The man I play is a retired teacher, who's widowed, and his son being blown up in a plane affects and changes him from being a lovable, nice, kind, caring human being into an angry person."
It is told in a series of flashbacks depicting the man's relationship with his son, and while the act of terrorism that so dramatically changes McCoy's character clearly derives from the 1988 Lockerbie bombing, it remains very much in the background.
"Lockerbie is there," says McCoy, "but it's not principal to the story. It's not a political play in that way, but there's the final straw that releases all this anger in him. One of the reasons for me wanting to do it was that I've got sons, and when I was reading it, I thought, well, how would I feel if that happened to me. I was touched."
Audiences may well have presumed McCoy to be touched in another way during his early days, when he flitted between risking life and limb in roadshow outings such as the self-explanatory An Evening With Sylvester McCoy The Human Bomb while becoming a kids TV regular.
"TV was very insular in those days," McCoy remembers, "and they didn't know much about theatre. But I was very lucky, because we'd become a bit of a cult by then, and Clive Doig, who did Vision On and created Jigsaw, had heard about this crazy guy exploding bombs in the Royal Court, and came to see me."
Fortunately for McCoy, Vision On was a mime artist down, and he got the gig. His double act with the late David Rappaport on the Janet Ellis-fronted Jigsaw as The O-Men tapped into the same sense of ad hoc anarchy that fuelled his work with Campbell, and it's easy in retrospect to see the influences of Buster Keaton, Max Wall, Stan Laurel and Alec Guinness, all of whom McCoy describes as his "gods".
Having a foot in such seemingly different camps also goes some way to explaining the peculiar post-1960s relationship between children's TV and the equally childlike first wave of British alternative theatre that was quietly subverting young minds while mum and dad were looking the other way. "I loved that schizophrenic existence," he says.
If things had worked out differently, McCoy could have been expounding another god after growing up an orphan, a factor he considers a crucial influence on how things turned out.
"Children who are brought up by their parents get their love by right, whereas if you're an orphan, you feel like you've got to earn it, so you try and be noticed more."
McCoy trained as a priest, "for a dare, and I loved every minute of it. I decided I wanted to be a Dominican monk, and really got into it. Method acting at its best. But I was a year too young, so was sent to a mixed school, and instead of wearing a skirt, I started chasing it."
McCoy got a job in the City, where he found himself drawn to swinging London's burgeoning scene based around the counter-culture's unofficial HQ, The Roundhouse.
"They needed a hippy who could count," McCoy says, "so I ended up working in the box office."
McCoy was recommended to Campbell by actor Brian Murphy, with whom he'd improvise little scenes around the box office. McCoy would run into Murphy again at the Theatre Royal Stratford a few years later, when legendary director Joan Littlewood hired him for a production of Brendan Behan's The Hostage after picking him up busking outside the theatre.
"I didn't know there were rules," McCoy says. "I only knew our rules, which was to grab that audience and shake them up. I was coming from a whole new energy and madness that was going on in fringe theatre, and at the time it freaked the others out. One of them even wrote to Equity to complain about me."
He and Leonard Fenton later made up, and ended up playing Beckett together.
McCoy's turn as The Fool in King Lear captured both sides of the comic pathos at which he's so adept. It's fitting, too, that Lear was played by Sir Ian McKellen, who played Gandalf in Lord of the Rings. This connection led to an invitation from Jackson on the New Zealand leg of the tour.
Having narrowly missed out on Lord of the Rings, McCoy was successful second time round, and after Plume returns to New Zealand to resume filming.
Beyond The Hobbit, McCoy expresses a desire to play Malvolio.
"He's funny," McCoy says, "but he's only funny because people laugh at him and not with him. He's kind of tragic and tortured, and they're the parts I seem to do best."
Plume, Tron Theatre, Glasgow, March 1-17 www.tron.co.uk