Originally Posted by Trevor

I doubt that this is under-voltage related. The brake warning light circuit incorporates a pair of diodes to block a sneak circuit. A faulty rectifier network within the alternator, will result in AC being generated and imposed on what are normally DC circuits. As a result this rogue voltage will bypass the diodes and illuminate the lamps.

N.B. I am not trying to show off my knowledge, or negate that which has been said, but rather to be informative. The diagnosis is perfectly correct, in that the alternator is the bad apple.