the easiest way to power the TV is to simple run an extension cord to an outlet that IS powered by the inverter, usually the FRIDGE outlet - you can't simply 'rewire' the inverter to make it work.
or the inverter itself may have it's own outlet that you can make use of...
'14 Palazzo 33.3 bunkhouse 34' diesel
KingTailgater2 Dish HD, 100w/5a SOLAR, BlueOx
100,000+mi since '14 - US, Alaska, Canada - Hiawassee, GA! (also, '14 Gulfstream Amerilite and '07 ForestRiver Rockwood) : )