I found some alternator diagram, but not from Toyota.
This is what can happen according to found diagram:
There are 3 diodes #3, sending voltage to rotor.
the voltage is applied to one side of battery light and there is ignition voltage on another side, no current going thru.
If one of the diodes fails to send voltage, 1/3 of time rotor wire works as ground for the light, so light is glowing with 1/3 of power (it is kind of like getting 4 volts instead of 12).
When your ignition is on, engine off, light is glowing 100%
Most of the time alternator can still work fine because regulator (not shown oin the diagram) tries to send more current thru rotor to compensate for dead diode.