I'd have to look at your specific wiring diagram, but in general, voltage is supplied to the light when the ignition switch is turned on, and it grounds itself through a circuit in the regulator as long as the alternator is not producing current. Once the voltage from the alternator rises to match or exceed battery voltage, equal voltage is applied to both wires, and the light goes out for lack of a ground.
It sounds like you might have a leaky diode in the alternator which allows a trickl drain on the battery when the vehicle sits for a while. Try disconnecting the heavy charge lead at the back of the alternator the next time you park the vehicle, and see if the parasitic drain goes away.
It's possible for an alternator to keep the battery charged during periods of light load even with one or two bad diodes, so a bench test by the average parts store guy might not find the problem.
Jerry
