I do believe that your car is the only year of the 123 series that has a KLIMA relay. This relay compares engine speed to compressor speed, and then cuts out the compressor if the speeds don't match. Lack of working tach, if related to no engine speed signal, would prevent the AC clutch from engaging.

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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