If my assumption is right, they used an already existing, easy to manage composite video signal, and used a custom plug.
Alternatively, they could be using a custom digital protocol which would make this a difficult endeavour.
If you have a multi-meter, you could set it to voltage and probe the jack on the back of the screen to determine if one of the pins provides power to the camera (which is likely). One of the other pins should be ground. The 3rd pin may be an analogue, or digital signal pin, we do not know yet. The last pin could be a complimentary signal pin, or an additional ground. Once more, we do not know yet.
Do you have access to an oscilloscope?
Do you have access to a spare camera, or are you confident enough to open the camera enclosure?
Edit: If you do decide to go probing, be sure not to accidentally short anything. If you are shy with your electronic skills, have another do it for you.