Let's go back to 1962 and the Broadway show, Little Me, which was one of those low-grade hits, winning some critical praise and one Tony Award. It lasted only 257 performances and among those involved in the production, there seems to be some disagreement as to whether it closed because the public stopped buying tickets or because its star, Sid Caesar, was tired of it. Caesar was pretty much the whole draw. He played seven different roles and, as one writer put it, "proved he could do anything on a stage except sing and dance."
The book was written by Neil Simon (his second Broadway show, following Come Blow Your Horn) and the songs were written by Carolyn Leigh and Cy Coleman, with Cy Feuer and Bob Fosse directing. Fosse also handled the choreography and in so doing, won the show's only Tony. The female lead was a character named Belle Poitrine who was played by Nancy Andrews in the present day and by Virginia Martin in flashbacks, and the plot followed her through her life with various husbands. In today's clip, I think the young man with the eyeshade is Mickey Deems, who had a very long career playing broad comedy parts in sitcoms and on stage. Here's ten and a half minutes of Little Me. I suspect this is from The Ed Sullivan Show but I don't know for sure.