On the last TT we had the tv was powered by a 12V "brick" supply. I got another connector for the tv, made a cable, and plugged it directly into the 12V jack on the antennae booster.
Fast forward - the new TT doesn't have a 12V outlet (GD, are you listening?) but that's been remedied. But the tv is 115VAC direct input, no separate power supply for it. I tried my PSW inverter on the new 12V power outlet but it squealed "low voltage."
OK, I had installed a deck-mount converter in the pass-through to suppliment the lousy factory WFCO one. I wired the inverter into the battery cables on the new converter. Now for the 115V side - I turned all the converter breakers off except for the main. Trial and error, but I found the breaker for the outlet for the tv. That's the only breaker "on." So, the TT main power cord is connected to the inverter and only powers the circuit the tv is on. It may be Rube Goldberg but it works. Now DW and granddaughter can watch a DVD together.