03 tahoe blower Moyer stays on all the time

[rockola1971]

Thats how the system works in these.

The power module (its not a resistor pack since you have auto climate control) will have 12 volts at it no matter what 24/7.

It receives a Pulse width modulated signal from the climate control head (on that tiny purple wire) and that tells the module what speed to run the blower.

Replace BOTH the module and the blower at the same time. Use OE parts here. The Dorman or aftermarket parts are crappy and you'll lose speeds with the power modules.
Aftermarket blowers tend to be loud/noisier than the ACdelco originals.

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It is actually still a "resistor pack", If you open one up you will will see multiple resistive wide traces on the circuit board. This is what is attached to the heat sink. They arent traditional wire wound power resistors but instead flat and essentially "painted" on the circuit board resistive elements. Evidently GM Engineers arent smart enough to use a triac or a SCR circuit.