Your turn signal probably is not flashing because the turn signal lightbulb is burnt out. You could also have a loose wire on the turn signal.
Turn on the RIGHT turn signal then get out of the vehicle and see which lights are flashing. Count the number of bulbs that are flashing on the back of the vehicle and on the front. Then turn on the LEFT turn signal and check again. Usually a rapid turn signal indicates that one or more bulb has failed.
A fast flashing turn signal, on most any vehicle, is an indicator that a turn signal bulb is going out or has gone out on that side(i.e. front turn signal on passenger side flashing fast, check the rear turn signal bulb on passenger side.) This will cause the light on your dash board to flash fast as well. This is generaly a good time to replace all of the bulbs, turn signal, running lights, and break lights, as they are so cheap. Also check deck light or top break light if applicable for burn outs.
You could be hitting the flash feature on the turn signal arm when you use it.
Bad flasher.
When it flashes fast it means you have a burned out bulb omn that side. Check all you lights and you'll find the one that's burned out.
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Both turn signals work when they want to. The hazzard lights work just fine. All bulbs are great. The turn signal indicator will flash inside the car for a few seconds and then stop. The outisde turn signal lights stop too.
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Turn signal indicators are lights. The flash to tell you, or indicate, that a turn signal is on, and which way the lights are flashing.
The airbag warning signal might flash on the Hyundai Sonata dashboard if the component is malfunctioning. It should be checked by a mechanic.
Burnt out bulb.
The Crucial Ballistic Tracer Memory is designed to add some flash and dazzle to their system. The most obvious and probably the cheapest place to buy one of these would be ebay.