You should not need to have the inverter switched on to watch TV when plugged into shore power. 2005 is the year that Roadtrek began to make the switch from a separate inverter unit and charger/converter unit to the Tripp-Lite single unit that does all three functions. If you have the Tripp-Lite then you certainly should not need to have the inverter wall switch on when plugged into shore power to have power in the outlet that shares the inverter. If you have the two separate units, then this design may have been different and then the inverter may need to be on to keep power to that outlet. My Roadtrek with the Tripp-Lite has an inverter switch on the wall. I understand that some earlier years did not have such a switch. This switch is connected to the Tripp-Lite as a remote - ON puts the unit into supplying inverted power OR charging batteries. OFF puts the unit into Charge Only mode in which it only charges the batteries and does not supply power to the outlet(s).