What must be done after applying the train air brakes during the train check process?

After applying the train air brakes during the train check process, it is essential to wait until the brake pipe exhaust has ceased. This step is crucial because it indicates that the air pressure in the brake pipe has stabilized after the application. If the exhaust is still occurring, it means that the brakes are still releasing and won't be fully applied until the exhaust ceases. This ensures that the brakes are properly set, allowing for accurate testing of the braking system's effectiveness. Waiting for this signal is a fundamental procedure to confirm that the train’s braking system is in optimal working condition before proceeding further with the inspection or operation. Ensuring that the exhaust has stopped helps in confirming that the air pressure has equalized throughout the system, leading to a safer and more reliable braking performance.