Mine came off completely as the black plastic bit needed replacing - can't remember if I cut the wire and reconected it - doubtful though. Perhaps the company who did it wernt sure if it came off.
I know that as the wire is coiled round under the roof lining, there isn't much give in the wire so takes a bit of effort to wiggle free.
Sorry I couldn't be more help - but its defo a roof lining down job for my car.