rear tail lights help!
You could get this behavior with the incorrect bulb model. (There are two filaments in the bulb and it sounds like only one of them is getting energized - except for the third brake light - with your running lights and brake lights are using the same filament.) Usually, your running lights would be one one filament and your brakes on another - which is why it gets "brighter."
To see what is going on, you might take the bulbs out of the lenses and watch the filaments (comparing them to the third brake light) to see what is going on.



