"Starter engaged" warning light
Another thread presented a sideline discussion on "starter engaged" warning lights. I did not realize that they were a requirement on UK aircraft - what a great idea! But, what do the supplements say about an illuminated light?
I would guess that the light indicates that the solenoid (contactor) which controls the starter motor, is energized, and presumably, that the motor is turning. Obviously, when this is unintended, it is bad, and is good cause for stopping the engine as soon as safely possible. Certainly these solenoids do stick engaged, and otherwise fail, so an indicator of their status is great, as long as the pilot knows what they are being told - The motor is energized.
However, every starter system includes a clutch or drive release of some kind, to engage, and disengage, the starter drive from the crankshaft. These mechanizms, in their various forms are every bit as troublesome as the solenoid, and their failure (usually a seizure) creates an even more unsafe situation.
When the stater motor, with an otherwise functional "clutch" does not stop running, because the solenoid has remained engaged, it is very likely that a Lycoming, or small continental engine will simply "over run" the starter drive, and operate more or less normally. Yes, the starter motor itself, is going to get really hot, and is certainly a fire and self destruction hazard, but otherwise, is not affecting the operation of the engine itself. The large Continental is a different matter.
A starter solenoid and motor can operate properly, and you can still have a starter problem, which is more serious, and costly.
In a Lycoming, a sticking "Bendix" happens from time to time. This means that the pinion which engages the ring gear, did not withdraw after the starter was de-energized. A careful pilot ear can sometimes hear the ringing howling sound of spinning Bendix. No warning light, but good cause to shut the engine down right away.
In Continentals, gears do not engage and disengage. The smaller Continentals, have an over running clutch, which are known to seize. When this happens, the starter motor is accelerated to a rotational speed far in excess of the design, and it's probably going to fly apart, and seize. This is going to cause something in the engine drive line to break. The larger Continentals employ a worm drive and clutch spring. These are known to seize and overheat. There are a number of reasons for, and variations on this failure, which are too much to describe here. In short, a running on motor in these engines is bad for several reasons, and there are other failures, which do not involve an energized motor.
So, just because your "starter engaged" warning light is not illuminated (it probably should be called a "starter energized" warning light), there could still be a failure of the starter system, which is every bit as serious. Be "at one" with how your engine should sound and operate just after start. If it is not right, shut it down, and have the maintainer have a look..