NO the 12v lighting circuit is not heavy enough wiring and TOO LONG of wire, too far from the batteries
just when you get interested in the movie or 'sports' broadcast
the voltage drop will cause the inverter to alarm or maybe shut down
a 300w continuous inverter is big enough
mount near the batteries, but NOT in the same compartment
run the 120v line from the inverter to the TV area
I can explain it to you.
But I Can Not understand it for you !
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1997 F53 Bounder 36s