Just a thought, but you may want to check your local regs regarding backup lights - they aren't legal on trailers here (BC, though it may be federal) and rear-facing white lights in general may be illuminated ONLY when in reverse gear.
A porch light on the back wall ought to be fine so long as it can't be activated from the TV.
At the risk of inflaming the discussion...if one wanted to charge the toad's battery from the TV, one could use an isolator made specifically for that job. They are cheap (~$50) and provide diode protection to prevent the batteries from backfeeding each other or the charging system...all without requiring any input from the driver or active switching of any kind.
They are standard equipment on boats with multiple banks and some allow the batteries to be tied together (paralleled) for emergency starts, though in this application I wouldn't try to run charge current from the toad's battery to the starter through a 10 or 12ga wire...
