After realizing the same thing, I've decided to make that third mouse button just a repeat of the first, accounting for righties and lefties alike when using them.
See, back in the old days, we used to get by with just two mouse buttons. You young'uns are just so goshdarned spoiled. Although I do have a trackman fx with 4 buttons, I only use three of them, and the third functions as the double click, which is something I COULD live without. Plus, on my arcade, I'll just be using mamewah anyway, so double clicking won't be needed...I think? Even if it is, I can live without.