A motor would be better, and much easier to use for testing the duty cycle, but you could also put a long wide ribbon or strip of un-gummed paper tape under the mouse (with the ball in place) and pull it out at as steady a speed as you can manage.
The next thing to do is either to print out that new photo A4 size, or use a paint program to edit it, and start labelling the signals (look in the Amiga manual for the mouse port pinout and use a DMM on continuity to identify each wire), and mark on it symbols and values for the top side components. If you have any difficulty identifying them post a high quality topside photo with the wires held out of the way. The electrolytic capacitor (little aluminum can in plastic sleeve) should have its value,and working voltage printed on its sleeve, together with a stripe to identify its negative lead.