My wife's 318i developed a mysterious gentle tapping last spring.  After
several hours driving and looking under the hood I discovered that it
was the climate control system.  When the temperature was set close to
ambient, the heater was clicking on/off courtesy of 2 solenoids mounted
in the engine bay on the firewall.  In cold weather, this hardly happens
because the solenoids are almost always open, and in warm weather,
always closed.

Try setting the temperature either very high or very low.  If it stops
tapping, or slows down, it's probably the cause.

We lived with it and it seemed to get quieter - or maybe we're used to
it now.

Chris