Since your dash tachometer works, the Klima box should be happy with that signal. Another thing which might disable the AC clutch is the kickdown switch under the accelerator pedal. If that switch stuck on, Klima would think you are accelerating hard so disable AC. Would likely also make the transmission stay in gears to higher rpms.

But test points in the wiring diagram to find which culprit in disabling the AC clutch. Some might be on the low-side (pressure switch?, forget). It isn't necessarily the Klima box. You could also remove it and actuate the clutch pin there with a jumper in the base.

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1984 & 1985 CA 300D's
1964 & 65 Mopar's - Valiant, Dart, Newport
1996 & 2002 Chrysler minivans