This is a system that works a little bit differently from the standard wheel, but, not by much. On the standard steering wheel you have two contact rings on the back of the steering wheel that are fixed. On the deluxe steering wheel you have one contact ring that fixed and another that 'floats'. The first picture is a picture of the horn button mechanism without the actual steering wheel. The second picture is the same thing, but, with the outer ring removed. On the inner ring you will notice that there are three teflon clips that have screw holes in them. On the front of steering wheel there are three screws with springs on them that hold that ring. Those springs are what makes the horn quit blowing when you release the horn button. That outer, fixed ring is also held on by three screws coming through the front of the steering wheel, but these are just plain, nothing special screws. No springs or anything. All that they do is hold that ring in place. In the second picture you also notice three tabs with contacts on them sticking out of the inner ring. When you press the horn button, those contacts touch the contacts on the outer ring and that completes the circuit to make the horns honk. When you release the horn button, those three springs pull the inner ring back to its rest position, breaking the circuit, and the horns quit honking. I have already posted the wiring diagrams and some suggestions on trouble-shooting the horns for problems that aren't caused by the actual horn button here.
http://thecareandfeedingofponies.blogspot.com/2008/03/horns-dont-work.html