Your 560SEL has the same basic switches and relays as the 260E.
Does your aux fan start running the minute you turn the key on? before you even start the engine? If so, you have a problem.
Please re-read and refer to the post I wrote originally. it has useful info, and will save me a lot of typing.
I personally see the temp. switch causing the problem mostly. on your car. The blue 2 pole temp switch that is used for high aux fan is located at the front of your engine, next to where the upper radiator hose attaches to the engine.
Let us know if you find anything, or have more questions.