Sounds like something other than a grounding issue. If the turn signals illuminate brightly as stated, the grounding should be adequate.
Normally, the turn signal and brake signal illuminate the SAME filament in a bulb. Almost sounds like there is some sort of mis-routing of the wiring. Normally, brake lights are routed thru the turn signal mechanism to allow the above to work, utilizing the same filament. It almost sounds like your brake wire is run to the dimmer-glowing taillight filament.
Those blue dot lenses aren't helping matters, either. DD