I think you should spend some time studying the service manual to see if you can glean some ideas.

Random thought: Is the blower motor pulling too much power and causing a self-protection circuit to engage?

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Respectfully,
/s/
M. Dillon
'87 124.193 (300TD) "White Whale", ~392k miles, 3.5l IP fitted
'95 124.131 (E300) "Sapphire", 380k miles
'73 Balboa 20 "Sanctification"
Charleston SC

While that is an interesting question.. why is the fan working at all in the first place when the push button controller is switch off?! It's crazy.

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87 300SDL
87 190D 2.5NA 5sp
90 300GD with 606 turbo!
08 GL320 CDI
12 ML350 Bluetec
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Past rides:
82 300SD - the one that started it all!
81 240D
87 300SDL - the first one.
92 300D 2.5 Turbo
99 E300 Turbodiesel
07 E320 Bluetec
12 S350 Bluetec