Generally if TV (tow vehicle ) has a 7 pin (RV style) connector it has 12 volts supplied to pin #4 ( black wire) that charges "break away" battery, by coincidence it is also same circuit that can charge larger high capacity 12 volt battery for trailer lighting and battery powered accessories.... Only issue may be to have some sort of diode isolation between small break away battery and main trailer battery so if you run down main battery you also do not discharge smaller brake battery...
IF TV is not wired for +12 volts on pin #4 (black) its usually standard practice to run wire from power source under hood through a fuse (30-40 amp) the through relay that is controlled by ignition switch that cuts off trailer battery system from TV system when engine is shut off in tow vehicle...
Also its wise to check that "ground" conductor, pin #1 (from plug to frame) of tow vehicle ( and trailer) is sufficient to carry "return load" for current (amp) rating of trailer/auxiliary/brake circuits.
Wiring up a 12 volt battery and lighting is a whole completely different thread and as you have probably noticed there is lots of information about "how to" here...
Dale
Lives his life vicariously through his own self.
Any statement made by me are strictly my own opinion.
You are free to ignore anything I say if you do not agree.
