My 2006 NT32 has a similar, nagging issue. When I took delivery of the boat in 2006, the fresh water pump (located on bulkhead in engine compartment), would kick on in a brief, one second, "burble". This usually happened at night, when pump usage was minimal. After the dealer checked for leaks (none found), they replace the water pump. The burble continued and the dealer replaced the pump, the 3rd one in a couple of days. When I got the boat to our home port, the burble continued. I finally found a hose leaking behind the vanity in the head. Tightened the hose clamp, and problem resolved. Fast forward to now, and the burble has started up again. Again, no leaks found. I find that if I run the pump at full pressure for a second, the burble will hold off for about 6 hours, so before going to sleep, I've been shutting down the pump at the circuit breaker.
Since I haven't found any leaks, this Winter I was planning to replace the pump, yet again. Before I do that, a friend told me yesterday that he had a similar issue on his NT with the Jabsco pump. Doing the check for leaks found nothing, but removing and cleaning the small screen filter attached to the pump cleared up the issue. Something was in the filter causing a pressure leak. Before I replace the pump, I will remove the screen filter, since I have a full-house water filter attached coming from the tank to the pump. I haven't cleaned out that small screen filter since I installed the full-house filter several years ago.