If the FD works while the RD doesn't, try swapping them around and see if the RD works if you plug it to the FD wire.
Tried that too! It seems to know which is which. So regardless of which shifter I plug into whatever hole it moves the same derailleur.
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Yes obviously, that's the whole point isn't it? It would allow you to determine whether the issue is in the derailleur or a different part of the system, depending on what happens after the switch. So in your case:
Begin: current FD works, RD doesn't
Swap: connect FD to RD wire, RD to FD wire
--> if the FD still shifts while being on the RD wire, the FD and the back wires are fine
--> if the FD doesn't shift while being on the RD wire, the issue is with the wire leading to the back of the bike
--> if the RD shifts while being on the FD wire, the RD and the front wires are fine so probably the wires reading to the back of the bike have issues
--> if the RD doesn't shift while being on the FD wire, the RD is broken
So I believe you would have reached the same conclusion like you did now.