Frost on Sundays, never started until September 1986, I was able to found that out in seconds......
He did co present the "The Sunday Programme" which run from 1985 until early 86, which it was replaced by jonathan Dimbleby on Sunday which went out from march - September 1986.
Well, it is true that Frost was on TVam on Sundays for most of its life, from 1983 to 1992, albeit not always billed as Frost on Sunday. My TV Times back issues have him presenting on Sunday mornings from the middle of 1983, after he moved off weekdays, but he only did it for six months of the year. At that point it was still billed as Good Morning Britain seven days a week but Frost's Sunday show was very much the format it had for the next two decades, so it's certainly not incorrect to say his Sunday show ran for virtually TVam's entire life, whatever it was called.
As the fantastic Morning Glory by Ian Jones points out, he alternated with Jonathan Dimbleby from the beginning of 1985, with the Frost on Sunday brand being introduced around that time, but it was only a rebranding, certainly not a new show. In the six months of the year he wasn't on, there were various other strands of a similar ilk, some better than others. At the beginning of 1989 there was TVam Reports with Adam Boulton but the ratings plummeted and Bruce Gyngell personally asked Anne Diamond to come back in its place.
Morning Glory points out that in September 1990, while the franchise bids were being made, Frost on Sunday came back for its longest ever run - thirty weeks - and was also shown on BSB. Of course Frost had a presence on BSB anyway, presenting their big opening night show and starring in their adverts. I don't know if it was ever shown on Sky News in this form.
But although his last show on TVam was indeed on Sunday 27th December 1992, that was his first appearance on the station for six months. His last proper programme was back in June, then for the summer they didn't have any live show on a Sunday, it was all repeats and imports while they were winding down. As the Radio Times points out, Maya Even, who was Frost's replacement in previous years, then did Even On Sunday from September, though only for an hour, 8-9am, while Frost had done a full ninety minutes. The RT does not bill this on Sky News. That lasted until the penultimate week before Frost came back for one last show. Then a week later he was on the Beeb, of course, which was shown an hour later on Sky News. Don't know when that stopped.