I've seen really weird issues with lights like that when a ground is bad somewhere. I had a car that had a similar type of issue and the root cause was a corroded ground in one of the bulb sockets. When you get a bad ground power will often find it's way to a ground through other bulbs, through switches when they are in certain positions, etc.
I know that doesn't help much.
Edit: I would pay special attention to the ground of the light that stays in the bright position. It could be that if the ground is missing, instead of power going across the "dim" filament and to ground, it goes across both filaments, and grounds through a switch somewhere. Just a thought. That is basically what was happening on the car I worked on.
Also, when you apply the brakes, does the "stuck bright" light go off completely? That would support the bad ground theory.
Last edited by BigTB; 03-10-2015 at 08:16 PM.