We had the exact scenario discussed, a private fire hydrant downstream of the pump was having water removed and the main booster pump would cycle on. However with what is being described, I would consider any check valves on the booster pump suction line. If there is a backflow prevention device it should be tested and/or inspected as well. In a normal situation the jockey pump kicks on and pushes everything up, the expected ways to relieve/lose pressure are (1) No water seen, the pipe and/or fittings are leaking in a place not seen-the underground (2) No water seen, the PRV on the discharge side of the booster pump (or on the systems) is set too low and is relieving pressure-not uncommon (3) No water seen, any/all of the supply side check valves are not water tight and the boosted pressure is leaking back into the lower pressure inlet (4) At the test header water is seen, have you confirmed that after the last fire pump test was the test header valve totally closed, often these can be left cracked open and this will drain pressure out the test header and most fitters leave the lowest test hose valve open and the cap loose so that condensate and leakage will not build up and freeze. If the test hdr valve is cracked and a hose valve cap loose there will be water building up under that hose valve.
If it is underground leaking there is a company called Leak Detectors in Illinois. I have used them 5~6 times in 34 years when we could not find the water leaks but Nelson works around the country and all I can say is he has always helped us AND he has helped those I recommended him to. I suspect he has some kind of electronic dowsing rod, he says no.