Its obvious that the manual is for another model than yours, so I wonder if you have the same buttons as in the manual, if not, then the red wire could be the "timer override" but its not mentioned anywhere.
OR it could be an ignition connection, to switch off all the lamps and displays when stopped.
OR someone did his own mod the kit.
There is however both tlf number and e-mail address in the manual, so talk to the guys.
You are right about the rest of the wires as sketched by you.
PS sounds as a nice piece of kit and well designed (apart from the missing wire in the manual)
May you enjoy peace and good health !