TV disabled with engine running

[WDW]

So I'm back on the topic of why our TV running offthe inverter is disabled when the engine started. I get why this might be a safety feature on the occasion where you could see the TV from the driver's position if someone was stupid enough to watch Jerry Springer and drive. However in our 31FK its way in the back and our intent was for the kids to be able to watch TV while were traveling. Interestingly enough the bedroom TV will operate off the generator even though there are no seatbelts back there! I know that in Winnebagos this is not an issue and the design floorplan is very similar. So having received previous advice about cutting "" the purple wire I did more investigation and pulled the socket apart today. as you can see from the picture the back of the receptacle has a small box which I've traced to the website of that manufacture to find that it is a relay. If you notice the romex coming out of the wall the white goes to the side of the receptacle in on the opposite side the copper ground goes to that pole. However the black romex coming out goes to that yellow wire nut and the jumper crosses throug the relay back to the receptacle. I didn't take the big plunge here and unhook that but my thoughts are that if I take that black wire and hook it directly to the receptacle bypassing that relay I should resolve my issue?
Anyone have a better handle on this?

[Paintinfool3]

I would take the wirenut off and pull those two apart test the one coming out of the romex to see if it is hot with the engine running and if it is then connect it to your receptacle