My door chime comes on when I turn on the headlights. It does this when the door is shut however. Any ideas? If the head lights are off, it stops. It works if the key is in the ignition and you open and close the door. But driving down the road with head lights on, it comes on.

 

Sounds like it's working as it should, with the exception of shutting up when the ign is on. The attached diagram is for an '86, might be same as yours, maybe the alarm isn't getting the ign signal from the Gauges fuse, or whatever it may have been called in the '91..

 

Had the same problem with my '89. If you don't even need it you can just yank it out like I did. If they didn't change anything between these years, there's a trap door thing under the driver side of the dash that flips down and the buzzer just pulls right out