Behind the Scenes
A listing for a half-hour "Behind the Scenes: Doctor Who", with the added description "A behind the scenes look at the making of this popular science-fiction series", was billed in papers for New York station WLIW on 14 April 1990, and for New Jersey Network on 24 October 1992.
As noted on that page, this is likely to be one of the shorts (possibly the one titled "Making of a Scene") recorded during the filming of the 1988 "Making of Silver Nemesis" special, the full version of which was aired by WLIW only a few months later, on 27 March, and again on 8 May 1993.
But if this was something else entirely, we are not sure what - but see the list of possibilities on our Documentaries and Specials page. (We are fairly sure that it wasn't Resistance is Useless, as that was screened by New Jersey Network two months later on 2 January 1993.)