I used the Furion back up camera on my trailer as well. When I received it, I tested it out in my truck before installing it. I just plugged it into the cigarette lighter which was its power supply. When I hooked it up to the trailer and went to use it, "It said no signal".
Did some more testing and called Furion and they had said the camera was bad. So I returned It back to Amazon. Which BTW was cheaper. So I ordered it from E trailer and tested it out as I did the first one. When it did the same thing saying "no signal", I contacted Etrailer. They had said that in order to get it to work in my truck, that I needed a 7 pin pigtail adapter. Which was $60. I complained because they asked what type of truck that I had and the trailer that I had. And had never said anything about this when purchasing the camera. They said it had something to do with GM.
I'm sorry but I cant remember what their exact wording was. But after it was sent to me all worked well.
If I would of known this earlier, I would of got my power supply elsewhere and kept the one from Amazon because it was a lot cheaper.
I know it is not like what your situation was but noticed that on your signature that you had a GMtruck