A 12 volt draw on battery from a one wire alternator

That "little box" attached to the Mopar alternator appears to be an aftermarket regulator, you need to find out what that is. Some of them, maybe all are a "one wire" setup.

You should be able to unhook the big black wire from the big stud at the alternator and "stop" the draw. That will confirm where it's coming form

No, you do not want your original regulator hooked up if that is the case

I DO NOT BELIEVE you can easily adapt that little regulator to a standard mopar alternator, which means you must reconnect your regulator. There should be a black rubber connector for it unless someone cut it off

The Mopar alternator has a green and a blue "push on" connects to the two field wires. Does not matter which one. The big black with eyelet goes to the big output stud.

You likely have more problems in the wiring