I too suspect it's the TV interlock line.... As Wizard said, the TV is supposed to be OFF when the engine is ON, my rig is wired that way... Many people cut the wire in order to allow the TV to be on.
Some of 'em get caught and pay big fines (I know this for a 3rd party fact.. I did not pay the fine, I gave the cop the section of law so he could write it on the ticket, Much nicer that way... Yes, that was (part of) My job)
NOTE: If that is what it is, I would leave it connected, and if you truly wish to have the TV on with the engine off.. Just plug it in elsewhere
Home is where I park it!