How is map light post to work?

Douse the map light post to only work with a door open?.... because it don't work with doors closed with switch up or down! I do have it hooked up wrong, I got the red wire hooked to the lighter & pink wire tap in to the red because someone has cut the plug off the pink that post to hook in the lighter, I did test hooking it up right with jumper wires, Map light steel douse the same!

Also with the doors open for a little bit the round key light time delay gets worm, is that normal?
Also my dome light gets about too hot to touch when you leave doors open a little bit, is that normal?...but its been like that for years before I even hooked my map light & glove box light back up.