'93 Buick LeSabre problem - interior lights stay on

I own a 1993 Buick Lesabre Limited. It just developed a problem. The interior lights stay on whether the engine is on or off. Normally, when you open a door the interior/courtesy lights stay on until you put the key in the ignition, then it goes off. It now stays on. By interior lights, I mean the overhead lamp (dual) and the lights in the front and rear door panels. Nothing on the dash remains lit and I don't get a problem showing up on the instrument panel. What could be causing this problem?

To prevent the battery from going dead I just removed the fuse that controls the interior lights and it did go out, but now I can't use the remote side mirror control, as they were on the same circuit as the interior lights. Please help.
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