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I would check the power distribution box near the battery for loose connections, bad grounds and flaky relays. Relays click when they have power applied or removed, or gain or lose their ground.
WRT the fuel pump, you can turn the key from off to on and the fuel pump should run for about 3-5 seconds. If you listen, you should hear it hum. It doesn't click, but the relay that energizes it may. There is also a relay that provides power to the computer, and I think there are several the GEM or SJB use to do such things as provide power after the key is turned to off, one-touch down drivers window, locks, etc
tom