There is a another strong possibility that no one has mentioned yet. We have established the pump is controlled by a pressure switch, which will activate the pump if the pressure in the pipework drops too low. As you describe the action of the pump as pulsing, its more than likely there is a leak somewhere. However it may not be a leak you can see.
Built into the pressure switch, is a non return valve. If the valve is not closing properly, then the pressure in the pipes can leak back past the NRV into the water container. No obvious sign of this type of leak as all the water stays in the pipes or water container, but the switch will detect the drop in pressure which activates the pumps, which builds the pressure and trips the pressure switch, and so on.
The solution is to carefully disassemble the pressure switch and NRV, clean it. look for any obvious damage. I can't recall if the NRV seals are available separately, but an email to Whale or call the local stockist should tell you. either repair the existing pressure switch or replace it.
,