The fast blinking means you have a blub out or a short in the system somewhere.
Probably a ground wire since you know the bulbs are good....
Just went through this. Things to check:
The bulb socket itself.
Ground wire in the harness that runs in the front of car.
Run a bridge wire from one turn signal ground to the other and see if it works then. If it does, you have a break in the ground wire that runs accross the front of the car.
You may have to do each of the 3 wire that connect to the turn signals to verify each one is working.
If it still doesn't work but all other lights and turn signals are working correctly, then I would have to say it's the bulb socket itself.
Everything else is working, correct ?
Let me know.