Why does the low voltage warning light not illuminate when the alt switch is on, but the engine is off?
If the ALT switch is not closed, but the BATT switch is closed, battery power is allowed to flow through the ALT FIELD breaker, through the Over Voltage warning light, and grounds through the Over Voltage Sensor.  If both the BATT and ALT switches are closed, current flows through both the ALT switch and maintains battery voltage at both terminals of the Over voltage warning light which prevents it from illuminating.  This design feature allows the Over voltage warning light to illuminate when either the alternator is not connected to the main electrical bus or the alternator is malfunctioning.