You could use DPDT switching jack sockets which have internal switches that are isolated from the jack itself but close or open their contacts automatically when you stick a jack in the socket. They are a bit tricky to get hold of and not cheap but i'm sure you could find them somewhere as they are commonly used on guitar cabs and amps.
If you wired the LED's on/off switching using the switching poles of the socket not connected to the jack, then you can turn them on or off by plugging in a jack.
Thats a really good idea, but i wouldn't like to undertake the wiring of that patchbay