I suspect you are correct that if I power off the inverter with the receptacle breaker off, I would lose power to the TV’s.
My concern is if I can turn off the 15A receptacle breaker and the TV’s don’t lose power with the inverter on, that would mean the inverter is powering the TV outlets directly without a breaker for protection.
If that is the case and there was a short or other problem with that circuit, there would be no breaker that trips and creates a possible fire hazard.
I think I will turn off the inverter and verify that turning off the 15A receptacle breaker powers off the TV’s. That will at least verify the TV circuit is protected when there is shore power or generator power.
I’d still like to think there is a breaker between the inverter AC output and the TV receptacles.
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