Possible bad alternator

I’ve had theft warning fuse pulled for a few years now. But since this charge light issue started last week I went and pulled all the fuses and relays and this bulb remains powered on when the car is off. Since the bulb is directly wired to the L terminal of the alternator I can only assume bad alternator that has an internal short would be the most likely way it could still have the bulb lit up. I just can’t find any info on the internal wiring of the alternator to know what the L terminal is connected to within the alternator normally. I’d assume the diodes or the regulator. And something has failed causing it to ground and turn on the bulb. With ignition switched to acc. Charge bulb should light up. In my car now it does the opposite. Charge bulb goes off when car is switched to acc

My car is doing opposite of what it should. With the key in the ignition and it turned to acc all of the lights should come on including the charge bulb. With the car off and key removed from ignition most lights should be off including the charge bulb. My charge bulb is on when the key is not in the ignition. If I put the key in the ignition and turn it to acc the charge bulb goes off. That is incorrect and I can only assume it’s a short from the alternator. Car otherwise starts and runs fine. Charge bulb is off while car is being driven and alternator is charging the battery. Th issue is really the charge bulb remaining powered on when the car is off and draining the battery. L terminal of alt is directly connected to that bulb but should keep the bulb off when car is off until ignition is switched on. I would guess Alt has gone bad and is shorting the L terminal somehow. Even with relays and fuses pulled the charge bulb remains on with car off.

FSM EL-25 says that with the ignition switch "on" and the charge light "off" that i need to disconnect the S,L Connector on the alt and ground the L lead wire. WHen i do that, if the light comes on for a Mitsubishi that i have a damaged IC-RG or bad A.C.G. obviously i will try that.. but from best i can tell.. that is what is happening when my car is completely off - that the L lead is being grounded by an internal short in the alt.. turning that light on despite the ignition being off.
They have an extra note in the FSM on that page to say "with alternator side L Terminal Grounded, internal short occurs when Positive Diode is short - circuited.
so i'm thinking that's my answer right there. I originally suspected that maybe i had a bad relay that was stuck and powering the bulb when it shouldn't but it looks like at the most basic level that bulb is wired direct to L terminal of alternator without going through any relay. Already have a new Alternator sitting here .. so will have to try what the FSM suggests.. i guess i can always hook up the new alt without removing the old alt just to see if the behaviour goes back to normal - of course once i've ruled out a short coming from somewhere else so i dont kill my new alt