Dome light, goes off when running, stays on when not
 

2002 Jeep Liberty 3.7 4wd sport.
I have a severe issue. My wife came in the other day and handed me one of the what they call rear window strut. It rusted out like they have in the past.It makes the rear window pop up that is above the tailgate. I am not sure if this has anything to do with my current problem with my dome lights. Now my dome lights front and rear stay on. I have checked the dimmer ect.. Get this, they go out when I start the car and go back on when i stop it. As far as i know, there is no wiring that goes to the rear window that pops up? I dont think its any of the contacts on the other doors. I cant see anything wrong with the tailgate or window contact when i close them. I am Losing my mind. Anyone with and idea, please let me know. Someone had the same problem on a previous thread but no answer was given and it was very old.
Respectfully,

remove rear hatch cover bet there a issue with the switch back there for the light ,might be a mercury switch in lock mech.

dome light
 

i was thinking that it may be that as well. Do I just replace the whole box(switch) If I have power befoe the box in the line, than its the box?
Thanks,
Jim

id unplug and see what happens you can always turn the light on by the switch.

I have this same exact problem!