Hmm, it would be highly unusual (and a real problem) if the fuel pump were to cycle under the circumstances you describe.
Instead, is it possible you're hearing the bilge pump cycling? Many so-called "smart" bilge pumps are over-designed (my opinion) Rube-Goldberg devices that needlessly cycle as you describe, and this is how they're designed to operate.
Additionally, if your cranking battery is nearing the end of it's useful life, this parasitic bilge pump cycling can result in a no-start over a relatively short period of time.