voltage output and flip flop output
Q1's gate is fed from a flip-flop hence it's fairly clear that Q1 is used as an enable control for Q4. When Q1 is off Q4's gate is pulled to 12 volts via R1 and this means that at the source of Q4 is a voltage of around 8 volts to 10 volts. 

I can't be more precise than this because Q4 is used as a source follower and the voltage it develops at the source is dependent on the gate threshold voltage of that MOSFET and the load current being taken through "wire" and "ring".

The voltage at "ring" is also current dependent because it is connected to ground via a 500 ohm potentiometer and this could be set to 500 ohms and drop 500 mV if 1 mA was flowing through "wire" and "ring".

So without knowing the current through "wire" and "ring" and the value if the potentiometer it's impossible to state what the voltage across them is.

Regarding the switch in red, if the circuit is currently driving current through "wire" and "ring" then closing the red switch will stop that current by turning off Q1 and this in turn simulates the current dropping as per what you say is the purpose of the circuit. On this basis, it seems to me like it functions as a "test" switch.

I think that this switch is part of the chip referred to as U24 and, as such U24 is probably an analogue switch controlled by another part of your circuit (unseen in your question).