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ORIGINAL: Greg in NWA AR

 Eureka!!! Problem discovered and resolved!!
I have seen many hits about this problem and figure many are experiencing the same.....GREAT NEWS!!! EASY FIX!!!!!   The problem is bad bulb sockets! I have discovered that if I removed the blue cover that holds the wires in the socket then pull out on the GROUND (black wire) then the bulb will flash on the correct filament.  
Now your asking OK how to make this fix permanent? 2 options as I see it.
1) Cut off the plastic protrusion on the blue cover that pushes the ground wire into the socket then put the cover back in place on the bulb socket and while pulling out the ground wire wrap tape around the ground to keep that outward tension on it.....I did this but doesn't last long.
2) Replace the bulb socket(s) as needed with OEM parts....I really like this best....Don't you?
Well that resloved my problem of the signal and brake light not operating on the correct filament. I must say that it was a long chase to final conclusion. I had rewired from the dash to the tail light unit, tested wiring till blue in the face, tried changing right unit with left unit and that's when I discovered it was in the light unit wiring....or so I thought....untill I finally found out the real cause was bad sockets....I was ready to torch the beasty and sell it to the insurance company just to regain some semblence of sanity....quirky little demon...
Hope this helps some of you out there ready to throw in the towel....like I was!
Enjoy!!!
Greg

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ORIGINAL: belagatyo

You did not list it, but I am sure, replaced the flasher too, right?

Fast blinking turn signals are almost always due to an open circuit, of which the most obvious is a blown bulb. Other causes can be corroded sockets and a faulty wiring harness. A thorough cleaning of the bulbs' sockets and all the associated connectors would be the first step to go. Once you've established that you have a good connection, smear a dab of silicone (tune-up) grease around to seal off moisture.