Do the horns work when you intentionally set off the alarm? If = YES, most of the horn system is functioning. Go to the next paragraph.
An 89 has a completely different horn button arrangement than the 90-96.
Pull the horn button off gently. It just pulls out. See if the little wire is still attached to the white tower sticking up through the steering wheel. If it isn't, the tang on the tower may be broken off. Happens when someone pulls too hard removing the horn button and the wire gets jerked out.
The tower piece used to be serviced by GM for a few bucks. It may still be. I've successfully cut a new slot into the tower with an exacto knife, but the steering wheel has to be removed and the contact ring and tower removed to work on it.