When running a 12 volt load the ability of the alternator to respond to that load is the critical factor. Seem as if that would be different than just charging the house battery
Regulator is going to respond to the overall voltage on the circuit being below it's target voltage, as long as the alternator has the capacity to deliver that plus a little left over you will charge rather than discharge.
I would imagine you could turn on the stuff you normally run in the TV and test voltage with a multi meter, then plug in trailer with fridge
on and re-test voltage. If it is in the normal range for alternator ( I think between 13.8 and 14.1 or something like that) then your set up is good. Don't think the difference between #12 and #8 would make it work or not work unless it was within about 8% of alternator capacity.
Installing new line for a 7 pin connector on TV I would go with #8 since the cost difference is minimal and 8% greater charge voltage is enough to be worth it. In my case the main purpose of that power line is to charge the battery
, Not going to be delivering an especially high charge rate anyway so every little bit helps.
Don't think I would be running fridge
on 12 volt going down the road. And would want to test first because I'm not sure if my alternator is high enough amperage to handle that if I'm running the blower for AC or heater, head lights
, wipers etc.