Thank you so much for the detailed and insightful reply. I disconnected the house battery and charged it using my car battery charger. It was up to over 13V when I stopped charging. Reconnected, then panel showed full charge. Drove RV back to our parking lot, then panel showed half charge. So, I think I'll replace the house battery. Incidentally, when I got to the lot, I tried the furnace, and it worked! So, I'll just have to wait and see if it fails again.
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