Q. What is the red wire at the head unit side of the supplied video extension cable?
The red (pigtail) wire at the base of the RCA jack at the head-end of the long extension cable is an optional trigger wire to trigger the monitor to display the backup camera when the gear is put in reverse.

A. Normally, the monitor switches to display the backup camera when the gear is put in reverse, the red wire can just be tidied up.

Otherwise, connect it to the rear camera (+) wire of the monitor (on the stereo system, it is usually the purple wire with a white stripe and labelled 'r/c' or 'r/c +'.

The red wire at the camera side is normally connected to the reverse wire to power the camera when the reverse backup light comes on.
This red wire wired to the backup light is continuous the red (pigtail) wire and the backup light turns on the red (pigtail) wire becomes hot, triggering the monitor to display the backup camera.