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You have already confirmed the reg as bad .
You state blower works fine if you ground the blue wire .. that by-passes the reg out of the circuit and verifies both blower power feed and good blower motor.
..and you state that you have trigger voltage [ yellow wire ] to the regulator.. that triggers the regulator, which is not happening b/c the reg is not conducting to ground even though it has trigger voltage.
.Diagnosis....bad reg...................................

Cheap out/temp fix ....... cabin ground switch on blue wire ... high fan only.