The mouse interface on the Amiga was remarkably and elegantly simple too, which would have made it easy to interpret the mouse inputs on a joystick port even if there wasn't built-in support for it.

Basically, the mouse buttons were wired directly to pins - the same pins that joystick buttons would be wired to. Then also, the left/right and up/down steps would be indicated by a rising pulse on one pin with a direction indicated on another pin. The same pins that would be used for the left/right and up/down microswitches on a joystick. The way this was implemented by most early mice was to have two sensors on a sense wheel slightly out of phase, so as the sense wheel rotated it would produce a square wave on both wires. When one pin had a rising pulse, the other wire would be high if the wheel was going in one direction, and low if it was going in the other direction.