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From your clues, I have deduced the logical answer to your puzzle. You went on a test run, came back and shut down. Without air flow through the engine compartment, and without a constant flow of fuel cooling the pump, heat soak began vaporizing the highly volatile fuel causing an intermittent release of vapor pressure from the outlet valve, much like steam in a boiling pot will vibrate the lid. With pressures equalized, the tick of the valve is momentarily silenced until pressure builds once again to the level required to release once more. As all conditions must be correct to produce this entertaining phenomenon, the elusive ticking sound quickly ends the performance until next it finds those precise conditions present.
Elementary, my dear Watson.