They are in their stock housing coming out of the camera, then they are apart for about half an inch as they go into a cat5 breakout board, then they are in a twisted cat5 pair for 8ft or so, then the reverse happens as they go into the LCD screen at the other end.
If you provide the 4A load with its own supply (with common earth) does this affect the problem?
Wait - you're not using impedance matching baluns
...also - video shield/signal "ground" should be kept separate from chassis/power ground, IIRC...
What size wire is used between the 12v battery and the 4a load, and how long is that wire?
Then it goes into a solid copper cat5 cable and back to pc