Alternator wiring circuit
Notice the green wire connects to a switched power source. The circuit contains a 500 ohm resistor in series between the switched power and the alternator. Connecting it to switched power keeps the regulator from drawing current when the engine is not running. The resistor limits the current flowing through the wire so that a fuse isn't needed if the wire shorts to ground.
Something is probably wired into the dash using the dimmer switch power feed. Look for aftermarket radio, stereo or alarm system to be the culprit.