The auxiliary water pump is there to help in the circulation of the coolant when the engine is at idle. The only thing that can stop hot coolant into the cabin is by using the temperature dial, which controls (I believe) the monovalve. Once the car is running the auxiliary pump is not needed.
What you hear clicking is a malfunction of the CCU circuit board itself.
Here is the remedy:
Take the CCU out, and resolder the contact points (most likely the push buttons).
Look closely for cracks at the solder points (cold solder). Very often with age they come apart, causing the intermittent switching on and off of the fan, and the ac compresor.
I am sure that is your problem. I had the same symptons over a year ago.
1999 Porsche 996 Carrera Convertible
1994 420E - SOLD
1986 300E - SOLD, what a car