Since this post I have installed a new battery in the jeep. I've been disconnecting the battery after I'm done with it just in case. With the new battery in, the ammeter still reads zero, and I've noticed that turning on the headlights moves the meter ever so slightly. I wasn't able to try the D-cell battery test that was suggested because getting behind that panel is a massive pain and I didn't think it was worth it. I think at this point, I'm just going to leave it and hope it all works.