I'd guess that either there is a burned out bulb on that side of the car, or your flasher has died. The flasher would affect both sides of the car though.
The most likely cause is the turn signal flasher.
Why would you want the blinker faster. They should blink at factory specs.
The tail light bulb is probably okay, it's the front signal light that is burned out, this would cause the rear light to blink rapid.
The emergency flashers and the signal lights are separate systems. Each has it's own fuse, switch and flasher relay. If your turn signals light up but don't blink I would blame the signal flasher relay.
The trun signal lever needs to be replaced.
That's usually an indication of a burned out bulb.
Make sure you check all the bulbs on the drivers side of your car. If you have a burnt out light bulb it won't blink. Try that. Hope it works.
The bulb that is not illuminating, is installed incorrectly. Take it out, and replace it with a new one, making sure the nubs on the socket are in the right slots.
Check your bulb, In the rear of the Generation 4 Ford Taurus, they use a single Dual filament bulb for the marker, turn signal, and brake functions. Chances are your bulb is burnt out and needs replacement.
With a scan tool, or try turning key on, off, on, off, on and counting the blinks of the check engine light. blink, blink, blink, pause, blink would be 31.
sounds like an electrical fault i would take it to a mechanic
it might need a new bulb - they often blink when they are about to die.