Mike,
Thank you for the input. The Gold Tone BZ-1000 link was the only link I could find of a mandolin with a guitar body. Nice to know you represent them.
The television show didn't show the head stock well enough to see the brand. According to the
+++ concert set list +++ the artists sung a cover of the Beatles "What Goes On" with Billy Strings on guitar and singing backing vocal and Molly Tuttle singing lead. I'm pretty sure she was playing the mandolin with acoustic guitar body instrument on this song.
The acoustic guitar body with Martin style head stock with four strings per side was what caught my eye even before they started playing. The acoustic body shape seems pretty rare.
The credits for the backing band ran by so fast on the screen I couldn't see who the musicians were. Dennis Crouch, Paul Franklin (steel guitar), Jim Keltner (drums), David Mansfield, Mike Rojas, Daniel Tashian.
Homer and Jethro were great comedians that were also serious jazz musicians. As a child I enjoyed their humor and as I grew older I learned to enjoy their music.