We cannot locate a water leak but when tank is full and we use water the pump turns on even when not drawing water. Can not see a visible leak in engine room.
If you are absolutly positive there are no leaks anywhere then your pump may not be holding pressure.
It could be elsewhere than in the ER, including any outside faucets like anchor rinse or transom showers. Also, if you have a diaphragm pump, debris in the valves can cause the pump to cycle on and off. Open the pump body and check the valves
One place to check is the regulator where you connect the city water. Mine was leaking there on the inside where the fresh water hose connects.
You have many places where you can have a leak. All sinks, showers, toilets, ice maker, sinks on bridge, aft deck shower head and even water heater. Make sure all is shut off, if pump still runs get a strong flash light and start searching. Also when you have shore water connection you would still have a leak, unless the leak is from your water tank to your pump.
The guys are right. Look everywhere. The boat is not that old but don't discount the possibility of the water heater tank corroding at the bottom. It only needs a pin hole to cause the water pump to cycle and may not be the easiest leak to find. Good luck.
You might want to check the check valve that should be between the pump and water tank. When it goes bad the pump can not hold pressure.