[A/S] brake controller question

[SHMossLanding@xxxxxxx]

I just purchased a 2000 GMC pick-up, rigged for a 5th wheel trailer.  It has 
a POD brake controller, which works fine. My question is, even with the key 
off while the trailer is connected the green light on the controller stays 
on.  Of course, it turns red when the brake is applied.  Is it normal for the 
light indicating a brake has been located to remain on all the time?

    We are leaving in the morning, and this is our first trip with the new 
truck, so if anyone knows,  could you write back soon.  I would hate to have 
a dead battery in the truck.

Thanks in advance,

       Chuck & Lynn
       1965 Overlander