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Barely hear it, but doesn't sound engine related, not steady enough.
Almost like a relay/solenoid clicking on and off.
After engine is cold, i.e. sitting overnight, loosen and remove fan belt from crank pulley
Start engine, you can run a cold engine for 2 minutes without water pump, Battery Light will be on.
Without the fan and pulley noises you should be able to hear noise better, if no noise then could be one of the pulleys, shut off engine and spin each pulley to see if you can find the noise.
Have a smaller diameter rubber hose handy, like a vacuum hose, these are good stethoscopes