There are no reported problems with the backup lamps on your vehicle. The problem coould be in the Intergrated Power Module (IPM), The Transmission Range Sensor (TRS) or the vehicles wiring. It is my recommendation that you have your local dealership inspect and diagnosis the vehicle as the electrical systems are very complex. It is difficult to give an estimate of labor costs when electrical issues are present as the diagnostic time can vary greatly. See you r local dealership for more information. They are best equipped to deal with our concern.