Hello Clive,
The Shureflow pump uses a displacement mechanaism to pump the water. It's a bit like a car engine, in that it has chambers (cylinders) and valves and displacers (pistons).
When the taps are wide open there is little resistance and the displacers can move relatively easily, and quietly (a bit like starting a car engine with the spark plugs out) the water will flow in and out of the chambers with minimum effort.
As soon as the taps begin to restrict or stop the water flow there is a considerable build up of resistance to the movement of the displacers, so the whole thing has to work harder, and that makes it louder. When it is doing this its not moving a lot of water but it is pressurising the water system.
The pump is controlled by a built in pressure switch, which whilst the pressure is low
(taps open) it make the pump run, and when the taps are closed the pump continues for a few moments until the pressure has built up enough to satisfy the switch, which in turn, turns off the pump.
The pipework in caravans is usually flexible plastic, and this will stretch just a bit if the fluid inside is under pressure, so just as the pressure builds up, the switch turns off the pump, but the pipework which is now under pressure creeps just a bit and it may be enough to drop the pressure and turn on the pump to restore the higher level.
Other things on the water system also have some give, for example in your water heater there is an air cap ( its designed to be there) this can also change its volume and if the hot tank is cooling the air cap pressure will drop and may cause the pump to run.
The pressure switch is usually adjustable (See the instructions for your pump) a small adjustment may stop the 'hunting'
On the face of it, there doesn't seem to be any thing wrong with what you describe, but obviously I cant see or hear your particular unit, so my explanation may not be the reason for your experience. You need someone with experience to actually listen and see what happening to have a better chance of resolving it for you.