It's still possible for the lights in the doors to not work because of this, they are on separate taps of that junction. But that alone wouldn't affect the overhead light.
I believe there's also something going on with the ground/switch side due to the "no 'ajar' light" condition.
True, but not a problem with the half working overhead light. And the ground is the only thing in common with all the partially/completely lights not working.