This issue could be caused by a faulty brake light switch or a problem with the wiring. When the key is in the accessory position, power is suppliedto the brake light switch, allowing the third brake light to function. However, when the key is turned on or the car is started, the switch may not be receiving power or may not be functioning properly, causing the third brake light to not workto the brake light switch and the third brake light, allowing it to function properly. However, when the key is turned on or the car is started, there may be a break in the wiring or a malfunction in the brake light switch, preventing the third brake light from functioning properly. The code PO573 indicates an issue with the brake pedal switch, which could also be contributing to the problem with the third brake light. It is recommended to have a professional mechanic diagnose and repair the issue to prevent any safety concerns while driving.