The starter warning light is not actually fitted to tell you that the starter is engaged. It actually shows that the stater solenoid is made.
The warning light is wired across the starter solenoid and lights up when power is supplied to the solenoid, i.e. on hitting the starter. If the solenoid jams in the engaged position it will quickly become very hot, and I mean hot. Jammed starter solenoids have been known to become so hot, that in one instance I know of, it melted its way through an oil tank, resulting in fire and total loss of the aircraft. The starter solenoid is not designed to take continous power, but rather intermittent. They should not be confused with the battery solenoid which is designed to take more power over a longer period.
The light should (must) go out as soon as you release the starter switch or key. If it stays on the solenoid may be sticking and should be investigated.
If the actual starter sticks in the engaged position the light will go out. You may be lucky and hear the tell tail high pitched whinning noise. In which case you case shut down. If not it will spin itself to death.
AC&X