I'd say that as long as the light goes out, everything's fine
Maybe I'm idle (well, yes, I am), but the fact that it goes out suggests that everything's working broadly ok, so I'd be tempted to leave it alone if it were mine.
Or #1:- Is the idle speed "about right"? If it's too low you could just turn it up a bit. You could check the tension on the generator belt, then look at the brushes in the generator (not bushes), the earth strap from the battery and the condition of the wiring between the generator and the battery itself. You would imagine that the regulator is regulating, from what you describe, so you could just gently polish the contacts on that a bit.
Or #2:- It is an awful, and dangerous, car that will soon catch fire and emit marble sized fireballs of death. Therefore, I will do the decent thing and buy it off you for three pounds, seven and sixpence.