I've left it open for long enough to have it time out and shut off.I believe the rear cargo light comes on when the tailgate is open, so most likely it would drain the battery. I have never left it open long enough to see if it would time out and shut off. I don't believe there is a shutoff switch. You could try leaving the tailgate open for 15-20 minutes and see if the light goes out. If it doesn't, then you have the answer you need.
I know it has been over a year but curious if this worked out for you? I got the same kind of tent and am going camping here. Hoping you had no issues and it turned off on its own.Thanks guys, now all that's left is to try it out in a couple weeks and have jumper cables just in case!