Thayer did some TV work during this period. He was a villain on The Wild, Wild West. He also did a TV adaptation of The Crucible, which featured Clarice Blackburn, Kathy Cody, Dana Elcar and John Harkins in supporting roles. Thayer also did a fair amount of theatre during this period. Some Broadway, some off Broadway.
A good deal of the time was spent with Holly Golightly, a musical adaptation of Breakfast at Tiffany's. It was produced by David Merrick, who had recently produced Hello, Dolly!, among other major successes. It starred Mary Tyler Moore and Richard Chamberlain, who had both just finished work on very popular series. The book was written Abe Burrows, who had written Guys and Dolls and lots of other plays. It should have been a success. But it bombed. Big time. It made it into NYC but closed after 4 previews.
I don't know if Thayer sang in the play. He played the part of Rusty Trawler. In the original film, the part was played by Stanley Adams. You may know Stanley from his role as Tybo, the giant talking carrot on Lost in Space.