Step 1 - Pull the ground wire out of the connector. Just pull. It will come out. (See the corrosion inside where the ground used to be? This caused problems!)

Step 2 - Solder a new piece of wire directly onto the appropriate raceway/path for the ground.

Step 3 - Add connectors to the end of the existing ground wire and new ground wire... I just used the kind that crimp down on the wire. Connect them.