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The size of the inverter you need to install, will determine the size of the power supply wiring and circuit protection ( fuse amps).
Inverter size will depend on the load from the TV and possibly other devices. ( DVD player ? )
TV type will be a factor too , so you need the TV manual to get it's power requirements.
If you can use a 400 Watt , inverter you should be able to tap into an existing circuit provided the wiring/fuse is adequate .
Anything larger , JMHO : I know it could be a PIA , but run a dedicated fused circuit . There may be a main power hub some where close that could be used , rather that go all the way to the batteries.