I think I see it now. Does the contact pin and spring fit into the turn signal canceling cam? Looking into the hole in the steering wheel the plastic looks kind of deteriorated (actually almost nonexistent). Would that possibly cause the horn circuit to short out and beep the horn as the canceling cam passes the turn signal contact?

I guess I've gotta take it apart to find out...

Gotta borrow a gear puller from the machine shop at work.