A/C compressor cycling?
Are you sure it isn't just the A/C compressor clutch cycling the compressor on and off? I don't know abut your model, but on my model this happens in all climate control positions except "EC". It could cause the idle speed to vary, and could cause the clicking sound you hear. Why don't you look at the A/C compressor and see if it's the culprit? You should be able to notice the end pulley start rotating and then stop rotating in accordance with your clicking noise.