It's Late Night with David Letterman! This is the 2nd episode it aired on Feb. 2nd 1982. Taped in 1993 after Letterman left NBC but before Conan started, for some reason, NBC re-aired the first two weeks of Dave's show.
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https://www.youtube.com/watch?v=FGrEl9dQiUA
This was one of the Cyberstar show tapes. The Cyberstar is the name of the system they used to run the shows for the Rock-afire Explosion on the late 80s. The shows prior to that ran off of reels (audio only) but the Cyberstar system was video based, so these little videos would play on monitors while the animatronics were performing.
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https://www.youtube.com/watch?v=EE39cLjMnBI