This is the perfect example for Finite State Maschine(s). So every switch interacts with the state machine and changes it. As it actually requires internal logic how such a switch board functions you would want to be able to change the 'wiring' any time and have the client be able to read the state machine. So in a more sophisticated approach you have a state definition (human and machine readable) that drives each 'simulation'. In that case the programmer wires everything up and you can finetune the state machine with the client. In a lesser approach you still use such an approach but only with human readable state machine (flowdiagram) and a nanimator/programmer needs to fix every little interaction going throught it.
Programs I'd recommend for programming are Hype (obviously) or Paint Code. If you use Hype you can use relative Timelines for the components of each FSM and it's state. The programming depends on the fact if you want a true FSM or only an if/else approximation.
Read about state machines here:
If that is to dry … look at
This is a very simple logic gate example (using rather the if/else approach then a FSM)
Since Hype 4 you can even use these switches as components
… look at