1. Burned out fuse
2. Burned out bulbs
3. Missing bulbs
4. Broken or shorted wiring
5. Defective turn signal switch
That's just for starters. Hard to say without more detailed information. What have you checked to this point? I'd first look at the fuse, then the bulbs, then do a voltage check with a multi-meter at the terminals to see if you even got voltage there. Start with one step, correct it and move to the next to find out what the problem is. Give us some more info and let's see what we can do.
The bulb housing might not be making a good ground. Wiggle the bulb socket while the turn signal is on and see if the bulb flashes. You might also have the wrong bulbs installed. I believe you need the 2-element bulb for them to work properly.
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