Yes, it does, but I leave it unplugged all the time unless I need the light which I never have. They are kind of famous for sticking on and killing batteries, so I always unplug them in our cars. When I put the custom hood on my old Roadtmaster I took that one off completely and pitched it.
Just a review point of your profile. Not much posted about yourself or RV. You say California, however, the time zone you are using is showing Al or Mississippi, LA area not CA, also not much showing for the years in the forum. Not even a proud photo of your unit. Happy Trails, keep it private I say after all we don't want Google, Facebook to know much about us on the web right?