According to lore, Deep 13 is actually located below Gizmonics Institute. There is a Deep 12, which housed some foxy neighbors for Dr. Forrester and TV's Frank. Dr. F's movie watching experiments were housed here, and Deep 13 was also where the broadcast controller for these experiments (called Mystery Science Theater 3000, in order to trick cable companies into thinking it was a program rather than an experiment) was housed. Deep 13 got a facelift in season 6 when Dr. F's mother came to visit, and it kept this new look until its final episode 706: Laserblast when Dr. F's funding was cut (funding?) and he was forced to move back in with his mother, leaving the Satellite of Love and it's crew to their own devices.
Former Best Brains employees have said that the Deep 13 set was so large that they couldn't keep it constantly standing like the SOL bridge, so they assembled it fresh for every shoot, and tore it down afterwards. Also, when the movie came out BBI sold copies of the flick and included a piece of the Deep 13 set with each one as a promo.