Randy also appeared as a solo act (with his band the Silverados, naturally) on the Midnight Special in December 1980, the Merv Griffin Show in August 1982 and Solid Gold in October 1982.
You can see a tantalizingly brief clip of the Merv show performance "Playing in the Deep End" during a segment for the American Journal tv program in 1994, available on the L&M site.
I've been searching high and low for the Merv and Solid Gold videos but no luck.