Ok. I made sure the batteries aren't reversed. I then disconnected everything completely from them. Measuring them I once again got 12.6V, so they are indeed charged. Batteries reconnected. I then removed the auto reset breaker entirely from the negative side and connected the two wires going to and from it together to get a connection to chassis. I measured from the negative lead of the battery to chassis ground and got a solid 12.6V. I tried plugging to shore power again with the batteries totally reconnected and am still getting the dimming, brightening, and toonnnggg! sound. The sound is coming from the converter.
It is actually going toonngg! then the lights brighten, then it goes click! when they dim. tooonnng! click! toooonnnnng! click!
I got my face real close to the converter to listen and let it just go like this for about a minute or two. After it had done it for a while I noticed the unmistakable scent of burning electronics. Although, this could just be the smell of the thing running and getting up to temp. I guess it's hard to say.
After that I disconnected the batteries completely again and tried with only shore power. I didn't try any of the 120VAC appliances. I just assumed they would work since they don't involve the batteries. With just shore power all of the 12VDC lights worked just fine with no toongs or clicks. Like they should.
I measured from the converter casing to the positive end of the fuses with only shore power and got about 7ish volts. When I measured this with the batteries hooked up it was 12.6V. Apparently it outputs less power with only shore power.
The converter just doesn't seem to want anything to do with the battery system. It seems to me like it's trying to feed back into the batteries to charge them but it just can't for some reason.
At this point I'm starting to think that the converter is bad.
Is it not good to just run everything on shore power? I barely use the lights anyway because I'm outside mostly when I camp. The main things for us are fridge and A/C anyway and those are all on AC voltage. Running the 12V system on just the converter I've heard is bad for the converter. At this point though I don't think it really matters, as the converter is probably bad anyways.
Any thoughts on this anyone?
Thanks again for all of your help and input everybody!