Here's what you should do to fix it:
1. Check the Bulbs: Start by visually inspecting all bulbs associated with the right rear turn signal. This includes:
* Right Rear Turn Signal Bulb: This is the most likely culprit.
* Right Rear Brake Light Bulb (if it's a dual-filament bulb): Some brake/turn signal bulbs have two filaments; one for the brake light and one for the turn signal. If the turn signal filament is burned out, the brake light might still work.
* Right Rear Running Light Bulb (if applicable): Though less likely, a failed running light could sometimes contribute to the problem, especially if it's a shared circuit.
2. Replace the Bulb(s): If you find a burnt-out bulb, replace it with a bulb of the correct wattage and type. Consult your owner's manual or a parts store for the correct bulb specifications. Pay close attention to how the bulb is oriented in its socket.
3. Check the Bulb Socket: While you're there, inspect the bulb socket for corrosion, damage, or loose connections. Clean the contacts with a wire brush or contact cleaner if necessary. Ensure the socket is properly seated in the housing.
4. Test the Fix: After replacing the bulb(s) and cleaning the socket, test the turn signals thoroughly. If the fast flashing persists, proceed to the next step.
5. Further Troubleshooting (If the problem persists): If replacing the bulb(s) and cleaning the socket doesn't solve the issue, the problem might be more complex, including:
* Wiring issue: A broken wire in the turn signal circuit could be causing the problem. You'll need to trace the wiring from the bulb socket back to the fuse box and the turn signal switch to identify any breaks or shorts. This requires some electrical knowledge and testing equipment (multimeter).
* Faulty Turn Signal Switch: Although less common, a faulty turn signal switch could also be the cause.
* Faulty Turn Signal Relay: A malfunctioning relay could interrupt the signal.
Important Safety Note: Before working on any automotive electrical system, disconnect the negative terminal of your car battery to prevent accidental shorts or shocks.
If you're not comfortable tackling electrical work yourself, take your car to a qualified mechanic. The initial bulb check and replacement is a simple and inexpensive fix, but more complex electrical faults require professional expertise.