If the starter is still engaged (Bendix stuck in) but the switch is released, does the light stay on?
Not necessarily. If power is still being applied because of a faulty switch or solenoid, then the light will illuminate.
However, if it is a jammed pinion then the light will not be illuminated, but the starter will be engaged and the engine will be spinning it. As the gear ratio is about 10:1 it will spin the starter at 10x the engine revs so can do a lot of damage. I have had one jam, and because the engine is driving the starter so fast I think heat is generated so the pinion jams further. The mechanic was unable to release it, even after removal from the aircraft. We had to fit a new starter.