Detecting paired node combinations
Connect all the shields to ground, so the only thing to detect is which center pins are connected to which other center pins.

This is pretty easy to do with scanning.  Set up the electronics so that each pin can be driven one way but passively pulled the other.  Since built-in pullups are more common in microcontrollers, I'll assume each line has a passive pullup and can be actively driven low.

Now you simply go thru the possible combinations.  Drive pin 1 low (all others passively pulled high), and read all the pins.  The one that is low is connected to pin 1.  Now drive pin 2 low and release all others and read all the pins, etc.

Let's say you do this slowly, like every 100 &micro;s.  Each 100 &micro;s interrupt you read the pins from the previous output state, then switch to the new output state.  That requires 12 interrupts or 1.2 ms to get the complete picture of what is connected to what.  That's way faster than humans can notice, so even at this slow scanning rate the processor will know what it connected to what instantaneously in human time.