Governor, pin + hole?

[Charles (49) Mo]

For the lack of not knowing exactly to call it, let me call it the "small governor output arm,with the spring", that has the external governor stub connected to it. This arm is pined to the output stub shaft by a 1/8"x5/8 steel pin. Problem is there is a difference of about 0.01" between the hole on the stub shaft and the dimension of the pin that connects the small arm to the shaft. The pin is tight in the arm holes, Miked at 0.125" or nominal 1/8" but the thru hole in the output stub shaft is +0.01" oversize, but uniform through-out. Sloppy fit,too much movement as I see it. Any experts have any knowledge to share as how tight the parts should be? Sorry for the long post...