First off you only need to connect the jumper wire if you are planning on using LED bulbs. If you're not switching over to LED bulbs just put the jumper wire to the side for future use and install the new board.
If you are going to use LED's, the reason you need to use the jumper wire is the SCR's have a higher turn on voltage because they were designed to work with the older filament light bulbs. LED's have a very low turn on voltage which can make the LED's look like there flickering or staying on if used on an older style lamp driver board. Your new board and the jumper will fix this issue.
You want to identify a control lamp on the back box. The easiest way is to put the game into self-test mode. Make sure your lamp driver board is connected up and turn on the game. Go ahead and push the self-test button. Just push the button once. The lamps should start flashing on and off. Identify one of the lamps on the back box that's flashing on and off. This is a control lamp. Now that you have identified a control lamp you now need to attach the bare end of the jumper wire. Turn the game off again.
So looking at the lamp socket that you have identified, it should look something like the picture below. Look for a fat solid color wire and a smaller striped wire. Take the wire that you just installed on TP13 on the LED/Lamp Driver Board and let's attach the other end of the wire which has already been stripped for your convenience. Wrap the bare wire around the braided wire that is attached to the fatter solid wire side. Now that you have the one side attached to the braided wire go ahead at this time and insert the terminal side of the jumper wire on TP13. You're done.