I was listening to the cast recording the other day, so I thought I'd post him singing, along with Susan Watson, one of the show's big hits, "A Lot of Livin' to Do."
Better still, here's a full, 14-minute clip of the show when it appeared on The Ed Sullivan Show. Dick Gautier comes in around the 4:25 mark. It's introduced by Dick Van Dyke (who later sings the big hit from the show, "Put On a Happy Face"), and features a lot of Paul Lynde. Why did the musical get such an incredibly long amount of time on the TV show? Well, if you know Bye Bye Birdie, you probably have a really good guess. The answer of which is included in this scene -- the song "Hymn for a Sunday Evening"...about appearing on The Ed Sullivan Show.