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The +12V in the trailer plug stays hot and is fused at 30 amps.
If you want something switched with the ignition you'll have to run something from the fuse box under the hood.
Chances are you will probably have to use a continuous duty solenoid or high capacity relay to switch power right from the battery to run the heater. Since you'll only need to power the coil side of the relay/solenoid you can probably tap off the power inverter circuit (should be switched w/ignition).