Sounds like a poor earth, remove the rear lenses and check the electrical connectors, this can also effect the turn signal lights as when you draw more current, either when the lights are on and then the extra current required for the brake lights and or turn signal lights these can go out/ dull or go out on particular circuits so its just a case of tracking down the electrical connectors that causing this.
I had similar, turn signal to right, tail lights went dim and all of them tried to blink.
Added additional ground wire to tail lights metal 'circuit board', after additional ground wire every thing worked normally.
A few days ago I noticed my rear flasher bulbs were losing their amber-ness, I replaced both, then found one was dimmer and flashing twice as fast. Dang. Took a look today, thinking about finding a good earth, applied some switch cleaner, no go. Put the old bulb back in, and it worked fine! So, I had bought a dodgy but not blown replacement bulb. Huh.