Battery charging from tow vehicle?

I was surprised to see that by the end of our first outing that our double 12 v batteries were discharged to almost 50% despite being connected to shore power. I'll be checking the installed converter to see if there is a problem. My question now though, is, by what route / mechanism are the batteries charged by the tow vehicle? Would a short or blown fuse in the converter prevent charging by the tow vehicle? Two hours home and the meter hadn't budged.  My 7-way wiring connector on the vehicle was unfortunately wired with nonstandard colors, but has six wires, which I assume have the typical lights, ground, the hot wire, and the brake controller wire. The center pole is empty which I believe is typically back up lights which of course the iPod does not have (hmmm...maybe a future nonstandard mod?  Can never seem to make it to a campground before dark. Anyhow...)

Hmmm....well that might be the issue with the the tow vehicle charge, we did have it in 12V mode to keep things from our Costco run cold on the way home. But I will get the meter out tonight....and need to check the converter/shore power issue too.

Thanks!