Welcome to the forum
A second water pump would a new one on me. When you run a faucet you will hear the pump and when you shut the faucet off you’ll hear the pump build pressure and shut off.
Are you hearing what sounds like another pump trying to build pressure? You may be hearing water lines vibrating against something, making you think it’s another pump. I would try grabbing the water lines under the sink with the pump on and see if the sound goes away or changes by moving them around.
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2012 Copper Canyon 273FWRET being towed by a 1994 Ford F350 CC,LB,Dually diesel.
Airlift 5000 bags, Prodigy brake control, 5 gauges on the pillar.Used to tow a '97 Jayco 323RKS.
Now an RVIA registered tech. Retired from Law enforcement in 2008 after 25+ yrs.