What I had forgotten in my years was the fact that battery need to be desulfated. Rather than go into a long disertation on batter sulfation, here is a
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I'm a little different in that I have chassis battery, and then house batteries. Those being equivalent to your TV and RV batteries. I was having a problem with the house batteries dropping voltage, even with the switches turned off. I purchased a Battery Minder and what a difference it made. I finally had to replace the house batteries when they checked bad.
You can purchase an inexpensive hydrometer and check your batteries for specific gravity. It's a simple process. It will give you an idea of their state. Only check them after a full charge and resting for 24 hours.
Good luck.