Thinking out loud:
It should not be that difficult to find the reverse switch wire, but now days who knows it could be a CAN communications bus.
If you found the wire, it's not too hard to make it activate from two places independently, but you also have to figure out if it goes to ground or + to activate.
Another option is to delay the off signal for the camera, say for a few minutes. So, it just stays on. A cooler, but more difficult OFF would be to turn off after 10 minutes or if the vehicle reaches 10 mph. Again, much harder but maybe more convenient and maybe impossible. It's just an idea.
Your other problem has two issues: 1) Switching video feeds and 2) The front camera would be non mirror image.
I think the camera or the monitor can do the reversal depending on the camera.
Can we assume NTSC or PAL standards or something else?
This could be really tough.
Here is an example of what's called a DIODE OR:
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Say the camera comes on when ground is supplied from the reverse switch. A diode can isolate the reverse switch and isolate your switch. SO, the switches don't interact. It may already have a diode there and you need to add an extra one.
See this:
http://www.clarkwire.com/TX-MVXManualRmtControlledVideoSwitch-2x1-BNC.htm
I'll add this as well:
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