Stuart
I think I have an AMX mouse somewhere, but it's likely in storage
However, the principles are not too hard to understand.
There are two signals for left / right, and two signals for up/down. I don't know what AMX called these signals, so I will call them X1, X2, Y1 and Y2.
So when you move the mouse in one direction, let's say left to right, X1 will pulse, then X2 will pulse. This sequence continues as long as you move the mouse. If you move it from right to left, X2 will pulse followed by X1. A similar thing happens with Y1 and Y2 in the up/down direction.
Assuming it has been cleaned. Apart from broken wires, poor connections, and cracked/dry jointed or broken solder connectons, the next most likely fault, is either one of the LEDs or one of the phototransistors having failed.
Can you take it to bits and take a photo of the PCB from both sides please.
Mark