I've been working on this for my dashcam for the past few weeks. You can see my findings in the thread where I'm searching for the fuse diagram.
The cigarette lighter socket is on when the car is on and will remain on for approximately 13 minutes after the car is off or last activity. It will come on if you lock/unlock the car. It is also on for the entire duration while the car is being charged. The glovebox light operates the same.
I'm still having some issues with my dashcam constantly rebooting. My most recent test is with a different power cable into the cigarette socket instead of the one I'm using for hardwire, but it is still rebooting. I'm not sure at this point if the issue is with cigarette lighter electrical circuit, the SD card, or the dashcam itself. Will keep testing...