Low battery light stays on with key removed

Yes, the battery light is on with the vehicle off and key removed from the ignition.

I'll do that in the morning. I am at home now and away from the shop.

Tested the wires highlighted showing 12v on b+ and nothing on the L wire.

I started the truck and it is hit when running. However, I noticed that the alternator is making a faint high pitched beeping noise with the truck off. Could this be a clue?

I need to add removing the connector will stop the noise but not turn the light off. I also started pulling fuses and checking to see if the light went out. I found that the light goes off when I pull the radio battery fuse. And of course the cluster fuse. Neither fuse stopped the alternator noise though. I am leaning towards a short or bad ground in the radio circuit. Am I on the right track?

I disconnected the main cable going to the alternator the noise stopped and the light went out. This told me the alternator was back feeding the light after the engine was off. So I replaced the alternator wired every thing up connected the battery and viola the same noise from. The new alternator and the low charge light is back on as well as the odometer stays on and the shift indicator. I'm still leaning towards something in the aftermarket radio might be to blame or in the ignition switch connector as changing that and the lock cylinder housing is what started this in the first place.

That makes sense I'll look at a new PCM. I am sure the price for that is going to be a tad expensive. Sorry to hear you've been sick hope your feeling better.

Just finished replacing the PCM with one I found online I just had to send the VIN in to get it programmed right. Plugged it in attached the battery cables did the pass-lock relearn procedure and she fired right up. No more lights on the dash and it actually seems to run better. Thanks for all of your help.