“People seem to enjoy the idea of me getting scared,” Don Knotts explained in the book Andy and Don. That’s why his first venture into feature films after leaving The Andy Griffith Show was The Ghost and Mr. Chicken, a 1966 comedy scripted by two of the sitcom’s writers and bearing more than a passing resemblance to “The Haunted House,” a Season Four episode that let Knotts show off his bug-eyed, terrified trembling to full effect.

But there’s one scene in The Ghost and Mr. Chicken that would never fly on the sitcom. After Knotts’ nervous character, Luther, is chased away from a cobweb-covered organ by a brood of animated bats, he discovers a painting of a woman who’s been stabbed with bloody garden shears. Luther’s eyes go wide, and then he faints.

If you think that sounds like Barney Fife behavior, think again. The Andy...