The two Prefab Sprout performances on Top of the Pops are well known, and widely available. Indeed we have them here.
But there is a third, and here, after a lot of hunting, it is. Scratchy VHS, yes, but really great to see, Martin and Paddy and some hired cowpokes in June 2001 (as shown on TOTP 2 on July 11th, 2001) singing Cowboy Dreams.
Second time for Paddy on the show performing this song, as he’d done it with Sting in the February 9th 1995 edition.