This pilgrimage to the 17th century landmark built at the behest of Charles 1 continued long after the Tron closed as a church in 1952, and only since the rise of large-scale Hogmanay events in the last 20 years did the tradition go into decline as the focus moved to Princes Street.
This year sees an attempt to revive the spirit of old Tron Kirk gatherings in the form of something styled as A Festival of the Extraordinary. Initiated and backed by the Drambuie drinks company, this three-day event runs from the night before to the morning after Hogmanay, and aims to bridge elements of the New Year tradition both old and new. This is done with a mixture of film screenings and performances in the daytime under the banner of The Drambuie Surreal Sessions, while the evenings are given over to club nights dubbed The Extraordinary Drambuie Gatherings.
The event's main visual focus will be a series of large-scale custom-built projections by Edinburgh-based digital artist and designer, Andy McGregor. His starting point is the iconography of Surrealism, an art form that is both subversively serious while remaining fun enough to be user-friendly.
"It's a genre I love," McGregor says, "and when this job came up I already had all the books on my shelf. If you look at Drambuie's recent ad campaign there are clear nods to Salvador Dali's dream sequence for Alfred Hitchcock's film, Spellbound, so that's a good starting point."
Images should include umbrellas raining from the inside, while a photo booth will project users' digitally realigned, portraits. A main theme will be following 72 hours in the life of a Hogmanay reveller.
"It's basically a 360-degree skyline of Edinburgh, but with things happening that you wouldn't normally expect," McGregor says. "I've filmed a journey through Edinburgh in different ways which people will be able to interact with, and make it strange or not strange as they move it backwards or forwards."
Films featured at the 9am free-to-enter screenings will include Tron, Whisky Galore and Hangover, while clubland institutions including Ultragroove take over at night. The original plan was that films would be shown using a vintage projector purloined from Glasgow's old Grosvenor cinema. At the time of writing, however, such is the projector's fragile state that transporting it between cities may well prove too delicate an operation for it to survive intact.
Working in The Tron's grand interior has left problems too for the team of 3D and 2D animators McGregor has drafted in to bring his vision to life. "It's an incredible space," he says, "but it's not without it's challenges. There are stained-glass windows which we can't touch, so although it's a 400ft canvas, there are places we have to work around. We're going to project on to the raw walls, so we're composing for the space rather than taking a straight cinematic approach."
With a background in international theatre with the likes of dance theatre company Bock and Vincenzi, McGregor is used to straddling the worlds of art and commerce in the way A Festival of the Extraordinary is attempting to do. By taking something with a fine art root and giving it a civic context, it may be a long way from 1950s celebrations at the Tron, but it retains a similarly populist draw.
"This is definitely crowd-pleasing stuff," says McGregor, "and there's absolutely nothing wrong with that."
A Festival of the Extraordinary, Tron Kirk, Edinburgh, December 30-January 1.