Ok could you send a picture of what that part is so i could possibly get a new one
Pics below (a '94 manual w/o tilt or cruise but yours, a '91, will be same or similar.)
From underneath remove 2 Phillips screws (deep in wells). Unsnap the upper and lower trim pieces and work them loose and out. Manual is easier than an auto; tilt may require repositioning the steering wheel during removal.
The multifunction switch is the big black honker in the pics.
Look at the wiring connectors before you buy a new one. Make sure they're not loose, and push in on the connectors and see if your lighting problems change. If either connector is melted or burnt you'll need to get a replacement pigtail harness.
Be careful with the connectors, especially unplugging them, as the plastic is old and brittle and the locking tabs will break if you if you're not REAL careful ! If the locking tabs are already broken, and the lighting problem is caused by the connector not seating, you can try tie-strapping the connector(s) tight or just get a replacement pigtail.
If the wiring is OK, you can remove the multifunction switch to take with you to the parts store; I think it's 2 7mm or 8mm hex screws to remove it.
It's not a hard job replacing it, just be careful, and disconnect the battery if you'd like to be sure that you don't short anything.
Good luck!