The BEHR clutch you installed will have this silly behaviour if its a similar part as used in the W124 E300D

It acts like a switch rather than a clutch, it will kick in at about gauge temperature of 95 and then only shut off at gauge temperature of 80. The US made horton brand works just right and smoothly engages in and out at the 90-95 temperature mark.

The horton one also blows some air at idle speed regardless of temperature (good for AC)

I remember seeing a shroud for the fan clutch of a 500 SEL, its a piece with round holes in it - supposedly to prevent extra fan engagement.

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2012 BMW X5 (Beef + Granite suspension model)

1995 E300D - The original humming machine (consumed by Flood 2017)
2000 E320 - The evolution (consumed by flood 2017)