The real cause is that the controller goes to full voltage several times per second for a brief period so that the RPM sensing circuit will work correctly. This dramatically changes the torque of the fan motor, which is where the click comes from.
Very informative & interesting, clearly stated!
Good luck finding a DC controller; I haven't seen one for several years.
As for me, I prefer the "good old" possibility to obtain 7V and 5V from standard MOLEX connector by simply interchanging the pins. 5V is directly on MOLEX and 7V is between 12V and 5V pins. With 12V (base), this gives you three speeds.
I do realize that this is no substitute for continuously variable controller though and it is not that much convenient to interchange the pins. Perhaps there is (should be) available some simple switch? (Molex on one side, than box with say just mechanical switches, 5V/7V/12V on output.)
EDIT: After reading viewtopic.php?f=9&t=22943
I learned that the "7V trick" mentioned above can be dangerous to the PSU, as you are feeding current back to PSU through 5V branch (thing the PSU is _NOT_ designed for). Anyhow, here is a how to with proper warning/explanation about the limitations of the "7V trick": http://www.silentpcreview.com/article6-page1.html