I found this as I was going down the Facebook wormhole. Eddie Van Halen sitting in with the band on Late Night With David Letterman May 16, 1985.
This clip has everything, Eddie smiling away as he jams with the band going to commercial, him playing a smoking instrumental of “Panama,” his wife, Valerie Bertinelli being interviewed by Letterman and telling an uncomfortable story of Paul Shaffer dating her when she was 16, then Sammy Hagar comes out to do a song. This clip is 31 minutes long but jump around for the good parts.
Paul Shaffer had so many great musicians appear on the show, but after Eddie passed he tweeted out, “Of all the guitarists I got to play with, he was my favorite.”
And Eddie, always smiling... Enjoy!