SIGNAL FLASHING FAST FRONT RIGHT NOTHING ON RIGHT REAR

SOURCE: right turn signal

have the same problem, sounds like you will need to get a new light socket (where the light bulb goes into).... it is a easy fix. cost approx $30-$50 at dealership for part

SOURCE: front signal light not working and rear signal

Your front turn signal socket is shot. Buy a new one at the dealer for about 30.00. It will fix it. You may be able to clean it and wiggle it to get it to work. But it wont last very long. I had the same problem. Replaced the socket and it is fine. Note: If one side is bad the other side it not far behind. Probably 2 or 3 months it will go also. Good Luck.
Bill

SOURCE: turn signals flashing too fast

Yes, This is easy. Recall on this problem. Take into dealer for free recall solution and it will stop.

SOURCE: rear left and right turn signal lights not working.

the electronic flasher module may be faulty, or you could have blown a fuse

SOURCE: I tried replacing the right rear turn signal

The circuit boards in Chevrolet tail lamps ar notorious for going bad. Dorman makes a replacement circuit board, part number 70006 . the same part number will fit either the left or right side of your Trailblazer.