Question to any fellow 2006 mustang owner...?
I don't have an '06 mustang, but what you describe occurs when one of the directional light bulbs is defective (or burned out).
The directional light interrupter speed is controlled by the amount of current going through it. The more current (2 or more bulbs) the slower it goes and the less current (only one bulb) the faster it goes.
Watch to see witch bulb is not flashing and replace it.