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No do not jump power to that wire, it is a signal wire. The resistor is built in to the circuitry of the blower it self. The blower motor will need to be replaced.
The climate control head sends a signal to the blower motor commanding it to come on from the blower's built in circuitry. The feed power and ground are indeed constant.
If you have a fast enough meter you can check the signal wire for voltage, you should not see full 12 volts but you will see varying activity.
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