PN 13621433077 is not fan switch, it is coolant temps sensor.
This part tells the Aux Fan when to runs high speed.

When this part goes bad (shorting out), the Aux fan runs all the time.
Not likely to be the problem in your case but I may be wrong.

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1998 E39 528i 5sp MT
2006 E53 X5 3.0 6sp MT