I also don't have that black ground wire screwed in the back of the cab.

My first thought is one of the two black wires from the right BR had come off, but both appear to be on yours. Also, the black closest to this mystery wire on your power supply board is also there. Lastly, both the blue caps have one wire each, as do yours. Here are my similar shots.

Good news is - whatever it connects to has to be within that wire's length. I'd take the end around in a circular motion, working outward from the center, and see if anything catches your eye.

EDIT: I also added a wide shot of everywhere it looks like your mystery wire could attach on my machine.

1 (resized).jpg
2 (resized).jpg

3 (resized).jpg

I saw nothing that would be that gauge of wire - they are all thicker down there - so it's not one that somehow became detached from a lug in the base.

It's possible this is a phantom wire as neither of us with the working cabs had it. If these things could talk to tell their tales!

1. Unlikely I'll get to this for a bit - wife now home from business trip and it's time for XMAS decorating. :/

2. Mentioned in above post that both my blue caps have one black each.

3. See #1.

Where does the other black wire go that's attached to the backboard there?

I'm still guessing this is a phantom wire - it just doesn't seem to belong anywhere based on two known working games.