I recently replaced my black wheel with an ivory wheel (complete including horn ring , backing plate, etc) for my 230SL and when I installed it the horn would go off fairly frequently. I thought I had tightened the nut too much so loosened it off and pulled the wheel off a bit. This seemed to sort out the problem for the most part but the horn would still sound, albiet infrequently, usually when I was stopped next to someone.
I didn't want to loosen the nut anymore so I took the whole wheel off and compared it to my original wheel. The pictures below illustrate what I had found, and I would have never guessed if I didn't have my original wheel as a comparison. The first picture is the underside of the original wheel and the second shows the replacement. You can see the extra raised ridges on the second picture, which is what depresses the horn contact plate on the steering column. I don't know if the one with the raised ridges comes from another car (W111 maybe?) or if there was a design change at some point. Maybe someone knows and can comment (Alfred or Achim?). This particular piece screws into and holds the chrome horn ring to the steering wheel. I just swapped out that particular piece (you don really see it) and put the wheel back on, tighened the nut and it is once again working as it should.
I thought I would share this in case anyone else runs into this situation.