Loudan Wainright iii wrote, composed and performed in a 1974 episode of M.A.S.H. titled "Rainbow Bridge," but had nothing to do with Suicide is Painless. The song he performed was titled "Oh Tokyo" as Hawkeye and Trapper John head off to Tokyo to regain some sanity after difficult times. I have found Oh Tokyo on YouTube, but no means of downloading it. It might not be a complete song. Either way, it's vintage Wainright.