The contact has a little nylon bump on it. When the cable is not plugged in, look down the backside of the contact for a small tab. You can bend this tab a little bit, but make sure that it isn't making contact when the cable isn't plugged in, or you'll just drain the battery.
If it doesn't work (or you break it) you can either replace the jack only, or replace the one-volume harness. The one-volume harness includes the volume control, battery clip and the output jack.
Also note that there's a new output jack. You can see it at the top of
this thread. You'll want to use the new one if it looks like there's enough room in your cavity for it.