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Why are you going to buy a new one before testing the old one ???…could be the module, a bad connection or the wiring…could also be the HVAC module itself…wiring below is for a 13 but should be the same as yours.
I assume to do a proper bench test you would need a PWM signal generator for the speed control?
As long as you have either an advanced DVOM that can read PWM in milliseconds or a scope it can be done without removing the motor...below pic is scope capture of a C5 I did a while back also with a PWM signal...power (blue), ground (red) and the PWM signal (green) were all checked.
Designer Imagines A Corvette That Looks More Like a Corvette Than the Corvette
Slideshow: A Jaguar designer's personal project imagines what a modern front-engined Corvette might look like if Chevrolet revisited the golden age of the Stingray.