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Fortunately my dual batteries are connected with the positive of one battery connected to the rig and the negative of the other battery is connected to ground (which is Method 2). I haven't checked the TV's dual batteries, but that's because I don't know if they are wired together or not and I am not too concerned.
I learned this lesson from a very smart Electronics college professor who was very good in warning us that a schematic doesn't always consider physics and the fact that "electricity likes to find the shortest distance for its journey" will be affected by this. Fortunately, I had him for several classes and we became good friends while I was in school. Plus he had a black late 50's/early 60's Porsche 356 that was cherried out and the envy of the parking lot. He only drove in two speeds, 0 or 60 and that was around the college. Even after 30 years I remember lots of things he taught us. The other professors, not so much.
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