Fuel valves are mechanical device operated by a solenoid coil when energize, it's a simple magnetism with moving core provided as an actuator called plunger, so everytime it's energize it produce a clicking sound. If I'm not mistaken there's shouldn't be a clicking sound if there's no movement or opening of valve. If the coil is energized and the plunger is stuck the sound is not noticeable. As far as the attempts to start your engine, the periodic repetition of on-and-off signal should brake-in your valve immediately. Although these valves require small amount of current but these are strong more than enough to pull the plunger. I've seen some solenoid valves failed due to long years of harsh operation but most of them stuck due to burned coil not the valve itself but those are for high voltage application. Your test also shown that there's no obstruction in the valve and fuel line as there's enough flow rate at the end of disconnected line. The only thing that you didn't test due to no access was from the inlet of starting gas to the burner...