What function does this gear on the winding wheel serve? It is hanging up and not allowing me to wind the watch. Is it supposed to do that? Thanks

That is a stopworks mechanism used on many of these earlier 12-size Howards, as well as many fine European watches and other early American watches. Its function is to restrict the mainspring to function only on the middle power range -- it prevents the spring from being fully wound or completely running down. If yours is preventing you from winding your watch it was either set up incorrectly or the mainspring has slipped or broken. Perhaps because of problems like this one often sees these with the stopworks removed - an unfortunate practice.

Thanks for your response. Well, I can wind the watch, the mechanism allows one revolution, then stops. I cleaned the watch and put a new mainspring in it. So, would I wind it up half way then put the gizmo on?

Ideally you would wind it up a few turns(maybe someone else knows how much) and then put the stopworks on so that it is at one of the two stopped positions, such that you can then wind it for five full turns of the barrel arbor before it stops on the other side of the convex stub. You will note that five of the arms of the stopwork are concave to pass the finger piece in the middle and only the convex arm stops the mechanism from progressing.

I have a similar Howard with stop works. I just wound it. It took 11 winds between my thumb and forefinger to fully wind. I don't know how many full revolutions that equates to.

It works pretty cool.