Leaving the 7 wire hooked up to the TT when the truck is off, has a level of issue pending the situation.
First is what brand TV you have. Yours and mine are GMís. On my 2003 Burb, the 7 wire battery lead in the 7 wire TV receptacle is hot all the time. It ties direct to the TV battery. On other brands some have reported of having a power relay in that same wire so when the ignition is off, so is the 7 wire power.
With this live all the time setup it can at times be a problem. Again it depends on the situation.
But here are a few without thinking real hard on it.
Essentially in the live all the time 7 wire receptacles on the TV, the TT battery is connected in parallel to the TV battery. When the TV is off, the 2 batteries will tend to want to equalize themselves. Current will flow from the stronger to the weaker as a load attempting to recharge the weaker one. If both are up to full charge, well it does not matter too much. If one is older and has a slight cell problem, it could draw from the stronger battery. Time is the factor here. Having this setup for a short while is not so much a problem. Having it all night long could turn out to leave the TV being drained if it was the stronger battery.
2nd case. You pull into a camp late and are leaving early. No shore power. So you run off the TT battery. Again if the TV has a live 7 wire, with the TV engine off, the camper is going to draw from both batteries and pull down both of them an amount of charge. How much depends on what you have powered up in the TT.
3rd case. You have the TV and TT hooked up at the house. Plug in the shore power to cool the fridge down the night before you go camping. If you leave the 7 wire plugged into the TV, the camper charger is attempting to charge both batteries and some brand converter chargers are not good at going into a float type mode. So over time, they can over charge either battery.
The common thing in these 3 examples if time. Short times are not so much a problem per say as every time you pull in for gas, or diesel (for some of those lucky TV pullers with a DuramaxÖ
) we do not even think about pulling the 7 wire plug. Or when we even go into a restaurant for lunch. As long as you do not have some large power draw in the TT going on, A Max air fan, a few lights left on, etc. this is normally not an issue.
However over night or many hours pending the draw on the TV battery, this leaving the 7 wire connected all the time could leave you in a not good situation. Cooking out the TV battery from over changing being plugged into shore power or draining the TV battery when not plugged in.
Key in this is to understand what is going where and if your 7 wire receptacle on the TV is hot all the time or not. Those with the power relay, do not have these same issues.
For me, I hook up the night before camping and cool the fridge on 120V. I also pull the 7 wire out of the TV and just plug it back when we leave.
To test to see if your 7 wire is hot all the time, if you have a 12 volt test light or a volt meter, just go out and put it on the pins in the 7 wire from battery to ground with TV off and you will see if you have power or not.
I have not been able to find any high power diode in the 7 wire battery feed line. If it is there, it is hiding on me.
What I have listed is not all encompassing nor will it fit every ones TV. This is just what I found out on my 2003 Chevy.
Hope this helps