I see in the picture below that the big black plastic connector (which is connected to my cigarette lighter case) is connected to what I only assume is the air con control? Also there is a double black cable connected to the case of the lighter. Is the set-up below correct?
Also would I be right in thinking if the twin black cable connector goes to the cigarette lighter case, is that the earth/neutral?

Photo used from another post I was reading about this issue.