Wiring my interior light - connector wire question.

I mentioned in another post that I mostly use the HF LED lights in my trailer, but there would be a certain charm to reaching inside, flipping the switch, and having the overhead come on.
I'm assuming that if I tap my batterie into one of the trailer connector wires, that the overhead will come on when not hooked up to the tow vehicle. (I bought it with a finished ceiling and insulated walls, so I can't just trace it back).
I found this diagram of color coded wiring, but it leaves me with another question.

The red says aux/charge, but if it's charging the backup brake battery, what keeps that battery out of the loop to keep it from lighting the overhead light in the first place?
Thanks for looking.
I'm assuming that if I tap my batterie into one of the trailer connector wires, that the overhead will come on when not hooked up to the tow vehicle. (I bought it with a finished ceiling and insulated walls, so I can't just trace it back).
I found this diagram of color coded wiring, but it leaves me with another question.

The red says aux/charge, but if it's charging the backup brake battery, what keeps that battery out of the loop to keep it from lighting the overhead light in the first place?
Thanks for looking.