Great question. A lot comes together at this point. Leading up to it, things are unraveling for Rumford. It has been proven that Springer couldn’t have cleaned the cannon because he wasn’t even around (he was at his girlfriend’s). And when Columbo suggests Rumford was the target, he asks the colonel to try and think back to someone that might have had a grudge against him. In trying to jog the colonel’s memory, Columbo puts forth a series of questions and one of them is “jealousy over a woman.” Here, unlike the other questions, Rumford offers up a quick, definitive “no.” This reactive dismissal and what it could signify has been discussed here before.
Then Rumford attempts to shift the relationship a bit by offering a cigar. Soon thereafter he asks Columbo if he has a first name. “My wife is about the only one who uses it,” says Columbo. By the time Rumford gets to the point about hanging up his uniform and taking care of his backyard, it’s pretty clear he is not married. Columbo’s reaction here is classic. He just harvested a series of answers to outstanding questions and missing pieces of the puzzle. Included here, as we see in the next scene, is the urinal-less locker room on the blueprint. The various layers of the onion come into focus: the colonel’s masculinity is really by persona/ front only and his grander mores of the military complex are so firmly fixed that he’s willing to commit murder to uphold them… “it had to be done and I’d do it again tomorrow.”