When I wind it, it makes no noise. Usually you hear the click, clicking. Could it be that the click has worn to the point of silencing itself?

Thanks,
Tom

Tom, I learned a long time ago, If it ain't broke, don't fix it. Sounds like the unit runs OK but you are curious. Is the clicker screw loose? Are all the teeth visually present on the gear? Let the unit down and check these things. Does the clicker have good return action? Kind of makes me think it might be a soft spring and the clicker return has lost it's snap.
Patrick

Patrick: Thanks for the reply. I looked at the one I'm questioning, as well as another. The first picture below is the quiet one. The second is one that is fine. Perhaps a more trained eye can see the differences, because I sure don't.

Other than the position of the screw slot, I see no difference. There could be a problem on the front side of the watch, but if it work's and returns like it is supposed to I would leave it alone as it's not going to effect the accuracy of the unit. Also, I notice a big difference in the two movement or case screws. It could be just an echo or resonance effect you are hearing.