I am not familiar with your exact setup. However, *most* camera installations utilize a camera controller module. The controller will have the R and L turn, and reverse sense wires going to it, and one video cable running from it to your monitor. The controller will also have a separate 12v power source. I agree with checking the ground (or 12v+) theory as being your problem is a good starting point for troubleshooting this, but if yours does indeed use a controller then I would try to find it as that is most likely where your loose or faulty ground or + wire problem is.
If your monitor has 3 different inputs, one for each camera, (no controller) then I would continue the direction you were heading with supplying a separate ground and even try a different 12v+ source as well temporarily to see if the problem goes away.
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