My '81 KZ 750 LTD's speedo stopped working
How do I tell if it's just the cable or if there's
a problem with the gearbox?
(Or something else?)

 

disconnect the cable and spin it and see if the gage moves, if it does then that would be your indication that its internal. im not sure how it connects but i did this on a buddys old gixxer and we figured it was in the sensor wheel and not the cabel or gage itself.

 

Some decision making/mechanical will tell you.

Cable:



Hub and assembly:

 

If the cable is hooked up and working properly, I would bet the Speedometer is bad. But taking apart and inspecting the mechanical sender at the wheel is very simple (And at no cost) to do.