I currently have a well house that has a 240V source on 12-2 wire powering a submersible well pump. I would like to wire in a 120V light. Can this be done using the 12-2 wire already in place or do I need to remove the 12-2 wire and install 12-3 wire? (It is approximately 60ft from the main house breaker to the well house and the wire runs underground.)

I understand that if I use 12-3 wire then, the neutral (white wire) is connected to the neutral strip of the panel, the two hots (black and red wire) come out from the double circuit breaker and the ground wire goes to the ground strip of the panel. At the well house, one hot and the neutral make the 120V for the light and the two hots make the 240V for the pump with no neutral. All grounds are connected together.

Hopefully, there is a way to wire in a 120V light with the 12-2 wire I already have in place.