A relay?

Did you try switching the wires on the LED strips?

It sounds like the door switch has a positive ground (I think that's the term).

 

I had the same issue for the back. So i put some led strip on top of the orange led amd got power from the dome light makes a big difference and i can see in the dark. Also put led strips in the trunk. The pic is the led trunk. Ill hey a pic of the led of the interior later.

 

Here is a pic of the interior led strip. It light enough that i can see the back and no cutting require.

 

anyone know the size for the 2 bulbs under the climate controls?

 

I added LED light strips on the back side of the B-pillars because there were no lights for the back seats. I wired them to the Map lights so I can turn the strips on and off with them.