Kevin,
Go pickup a copy of Corvette Fever, Sept 2004 issue on your newstand now.
Under the Shark Bites section is an article from a guy having trouble with his horns. It has a good explanation of how the system works and some things to check. It sounds like your problem is in the steering column, have you had the horn button off lately?
Get a Clymer or Chilton manual (cheap) that has wiring diagrams in the back as backup.
Sometimes all the garbage in the steering column gets gummed up, parts wear, parts broken, etc. Think how many times you move the steering wheel and the horn doesn't sound, thats alot of use....other than that, I suggest you at least wave when it goes off unexpectedly, looks better than honking and not waving.
Let us know how it goes, we'll help all we can.