Can't figure why the solenoid would be clicking in the pits with the car off unless there is an electrical contact being made (even with the switch and light off)
I do believe he means when he hits the button with the engine off........tough to hear it otherwise.
I had a Moroso unit do this to me......went back the the Hurst and should have went with it from the start.
I used one on our last deal for a dozen trouble free years.
Got cheap with this car and had to pay twice........I don't think I got six months out of it before it failed.
I never did find if it was debris or electrical or just a sticky valve.......but it gradually released pressure.
Took a couple minutes to release.