In 1967, Conway was cast in the title role of a western comedy series, “Rango,” about a Texas Ranger who, assigned to a desolate ranger station, manages to attract trouble where there hadn’t been any.

It was the first of several shows starring Conway that did not last long, among them two variety series, “The Tim Conway Comedy Hour” (1970) and “The Tim Conway Show” (1980-81). Conway was not unaware ...