Defective flasher relay.
Turn on that fast blinking signal light and check to see if the front and rear signal lights are both working, chances are you have a burned out bulb. If both front and rear bulbs are flashing fast, replace the flasher relay.
A bulb has burnt out that is why it is blinking fast. Check the front and rear bulbs.
Replace the signal flasher relay assuming you have physically seen front and rear, left and right signal bulbs flash.
A fast turn signal blinking can be caused by a bulb that is getting ready to out or a bad ground. Remove the bulbs and look for corrosion around the base and in the bulb socket.
Front signal bulbs on a RSX are changed from the engine bay. Find the lightbulbs for the signal bulbs located towards the bumper of the vehicle. Pull them out and replace them.
Double check the bulbs you replaced, you may have installed one incorrectly or one of the bulbs is faulty. See sources and related links below for bulb information. I have seen that the turn signal flasher can cause this to occur. One side flashes faster than the other side even though all bulbs are working. The remedy is to replace the flasher unit.
Check that there are no burnt out bulbs. Some vehicles will either blink the turn signal faster or not at all, depending on whether the front or rear bulb is burned out. If all bulbs are functional, try replacing the flasher unit.
One or two front turn signal bulbs is busted. Check your front turn signal bulbs and replace it.
That means either the Front or rear bulb is not working and needs to be replaced.
Most of the time, a non-blinking turn signal simply means that one of your turn signal bulbs is not working. On many cars, the non-working bulb may not be obvious, i.e. it could be one of the small side marker lights rather than a front or rear turn signal bulb, so look carefully.
One of the bulbs is burned out on the left side. The left front or rear bulb is burned out. Same problem with left side blinking rapidly and right side blinking normal speed. Both left side bulbs are lighting up, however?? Replaced both anyway and the problem still exists.
It has been my experience that a rapid turn signal indicates there is a burnt-out signal light bulb (either front or rear) on the side of the rapid blinking signal. If the right signal is blinking rapidly, the problem is in the signal lights for the right side (front or rear) of the vehicle. Turn the rapid signal on and step out of the vehicle to find which bulb is not lighting.