Cycle end pump
In these cases, the rainwater unit's automatic switch registers the pressure drop and switches the pump on correctly. However, as the flow rate is too low, the pump switches off again a short time later.
Eliminate the cause, because continuous cycling damages the pump. Specifically, the capacitor, an electrical component contained in most pumps, is suffering.
To check whether the cause of the pulsing is really a leak in the pipework, you can close the (hopefully existing) gate valve or ball valve at the outlet of your rainwater unit. This disconnects the rainwater unit from the domestic pipework. The pulsing should stop. If this is the case, check the pipework system and the connected tapping points for leaks and eliminate them.