Depends on how this ignition switch work in you simulator.

If allow assign a key for each postion (L - R - Both - Start):

Wire L, R, Both and Start in 4 buttons input in Arduino (MMjoy2).

- An way to make "Start" position momentary, using an key and spring, attached to rotary switch.

https://cessna172sim.allanglen.com/docs/key-switch/

If the sim use only 2 buttons/keys, one for "next" and one for "previous", try set this rotary switch for emulate an encoder, see here how:

http://www.737ng.co.uk/simple%20encoder.pdf
http://www.737ng.co.uk/switch_as_encoder.pdf

You wire rotary switch in 2 buttons inputs of Arduino - using the "truth table" and set this 2 buttons inputs as encoder in MMJoySetup.