which pump in our E60 diesel is not a constant flow pump?

I hear a pump noise that sounds like a plunger pump from my engine. It has no real constant rhythm. It is only heard when the engine idles. It is only heard when the engine has reached optimum temperature.

This is bugging me, not sure if it is the water pump that's about to fail. Is the water pump a type of plunger pump that could give this noise? I thought car water pumps were constant flow pumps that gave a constant "grinding noise" when they began to fail.

Car is working fine though with no errors on idrive