Hey Oregon Pacman, I remember you from KLOV. Welcome.
There are 13 pins on the connector, and they ALMOST wire straight across. There is one pin that changes position. If you hold the joystick upside down, so the handle is pointing at the ground and the pins are pointing at your gut, label the pins 1-13 from left to right. Pin #7 (the middle one) moves to the #13 position at the other end of the harness, and pins 8-13 all move down one position. I haven't checked, but I'd be willing to bet that's the common ground pin.
Like so:
1 2 3 4 5 6 7 8 9 10 11 12 13 (joystick)
1 2 3 4 5 6 8 9 10 11 12 13 7 (PCB)
Or at least, that's the way it is on my Bermuda Triangle machine.