Her is the circuit that I put together that allows the car or caravan connector to be used for reverse and detecting the presences of the caravan and using the correct camera and also being able to select either camera. I have not used it and may not as I have changed GPS and may be able to use multiple inputs and the reversing wire on the GPS.
This design was more for a single input GPS that detected a video feed on the video input and would switch it in.
There are two options, the second one uses a double pole triple throw (DPTT) switch. The problem with this was that I could not readily find a switch that looked the part and was actually DPTT. They are all On/Off/On which is different.
So a quick how it works (using the first option with two relays:
Switch in Off position gives you automatic reverse, GPS detects video feed and displays.
No caravan connected
When reverse is activated power goes through Relay 1 (NC) down to A does not activate Relay 2 as the caravan is not connected, but is looped to the contacts of the relay and supplies power to B which then supplies power to the car camera.
This also activates D put this goes no where as it is isolated by the switch.
With caravan connected
When reverse is activated power goes through Relay 1 (NC) down to A and as the caravan connection closes the loop in the connector it activates Relay 2 (NO) and supplies power to C which then activates the caravan camera.
This also activates E put this goes no where as it is isolated by the switch.
Switch in Up position powers the caravan camera all the time
Put the Switch into the up position will via one set of contacts engage Relay 1 and isolate the reversing input so it has no effect.
This will also via the second set of contacts supply power directly to the caravan camera via E.
This will also activate C which is isolated by the Normally Open (NO) contact on relay 2 and relay 2 can not be activated because of A being isolated by relay 1.
Switch in Down position powers the car camera all the time
Put the Switch into the down position will via one set of contacts engage Relay 1 and isolate the reversing input so it has no effect.
This will also via the second set of contacts supply power directly to the car camera via D.
This will also activate B which will via the Normally Closed (NC) contact activate A which will activate the contact of relay 1 but is is isolated by the Normally Open (NC) contact on relay 1 being open as relay 1 is activated.
The line through the middle was my initial cut at dividing the system between front and back of car.
Also you need to determine if the switching for reverse is positive side or negative. This circuit assumes that reverse is activated by the reverse feed going 12V. If the reverse is activated by the reverse feed going 0V (Earth) than you need to change the 12 V Reverse input and the loop ground around.
And finally the video feed would go through a combiner / splitter (passive device) and feed the reverse input for your GPS reversing camera.
Note that I have not installed this and you need to know the reversing polarity of your car, the load that the relays and camera will put on the circuits and that this is acceptable and that the GPS will take the feed over the distance and through the splitter / combiner.
If I implement this then I will be laying it all out prior to installation and connecting it up to make sure it all works. I would then package it all up and check again then install.