+2That is normal for the tailgate. At least mine acts the same way that yours does. With the tailgate flipped down, you can turn on the cargo lights with the buttons that are at the lower end of the grab handles.
I dont have a door agar light on the dash. Maybe its burnt out.
Mine works same way. tailgate down - no lights, tailgate swung to the side - lights on.
I recently worked on my cluster for other issues and noticed the bulb for "door ajar" was missing. I put in a bulb, and it works now.
I have to slam the tailgate really hard to make the lights go out. I have been meaning to disable the the light switch in the tailgate to the grab handle lights. The manual button would still work.