Interior lights won't go off when doors close

When car doors are opened and then closed, interior lights will not go off–until I unplug battery cable. Then they go off and stay off until doors are opened again. I have replaced both door light on/off switches.

Do you have a suggestion?

What year Cadillac?

If the interior light is the “old fashioned” type on the ceiling of the car, it likely has a three-position switch–off, on continually, and on when doors are opened/off when doors are closed. If you have this type of light switch, and if anyone recently “played” with the switch, it could simply be in the wrong position.
Yes, I know that this is overly simplistic, but sometimes the really simple fixes are the ones that work.

1980 Coupe de Ville

1980 Coupe de Ville

Since you have to remove the power to the lights in order to turn them off I assume there is a light control module for the lights. It may normally dim the lights down when the doors close. I would suspect the trouble is within the module if there is one.