was the guy who played him also playing the father on DENNIS THE MENACE at the same time? I know the same guy played both roles.

Herbert Anderson was the father on DTM, and I think the TAGS guy you're thinking of is Olan Soule. Both are character actors (other than Anderson's top billing on DTM) and both have been on a lot of shows.

Go to imdb.com or it's app. It's loaded with great information on shows, episodes, and it's actors. I've looked up Olan Soule many times there.

Olan Soule also played the hotel clerk in the episode in which the Darling Family stayed overnight in Mayberry.