Does, or did, the house use fuel oil for heating? WATCHMAN oil tank alarms are used to detect a rapid drop in the tank level that would indicate a theft in progress.

Can you tell where the wiring leads to?

Could be a panic bell, similar to a burglar alarm, but requires manual activation.

Occupant opens the door, visitor won’t go away. Occupant presses a button.

Popular in the early 60’s in my neighborhood, the suburbs. I remember a neighbor showing his granddaughter how to use it. Was just after the nursing students were killed in Chicago....maybe mid 60’s.

Classic burglar alarm?