What action should be taken to check the functioning of the parking brake valve?

To assess the functioning of the parking brake valve, the correct action involves pumping down the service brake until the valve pops out. This process is crucial because it allows the operator to verify that the parking brake valve is engaging and disengaging properly. When the service brake is pumped down, it creates a situation where the brake pressure is lowered, prompting the valve to respond. If the valve operates as intended, it will extend and indicate that the parking brake system is functioning correctly.

In contrast, other options do not serve the purpose of checking the parking brake valve. Pressing the accelerator pedal does not evaluate any brake system component; rather, it only increases engine speed without providing information on the brake system's integrity. Releasing the parking brake does not assess the valve’s functionality either; it simply disengages the brake without providing any feedback on the valve's operation. Monitoring the fuel gauge, while important for vehicle operation, is unrelated to the assessment of the braking system. Therefore, only pumping down the service brake to observe the valve's response directly tests the parking brake valve's effectiveness.