The problem is at that connector or before, in the fuse box itself.
Could be a fuse holder for the dome / courtesy not making good connection. The orange wire IS supposed to allways be hot, the white is ground.
When the door closes the other lights pass 12 volts through the filaments to the white wire. If you ground the white wire the lights will turn on.
The problem is in the fuse box,either a fuse holder or a buss bar is broken .
Fact is stranger than Fiction