Constant 12v, 12v is on when car is off. Ignition on 12v, power only comes on when car is on. Since Tesla can charge the 12v, in theory you don't have to worry about drainage except it might eat some of the big battery.
I have been running it via the trailer plug with the 12v constantly on. No problem except for the memory card not lasting all that long. Heat doesn't seem to be an issue with the F800 Pro as it is on a capacitor. I don't think you should do it to one that runs off battery.