Eight times a week, Alex Winter takes the stage in a bowler hat and an expression of marked confusion. He is Vladimir, one half of a curious pair of fellows anticipating the arrival of one Mr. Godot.

Let’s go back in time — to 1989 — when movie-goers first met the dopey but adorable time-traveling headbangers in “Bill & Ted’s Excellent Adventure.” The film put actors Keanu Reeves and Alex Winter ...