I wouldn't waste time with nylon cords anymore when fixing these antennas. Inevitably, they will break and you'll be pulling it out. Even buying NOS. Might not been a problem while they were still making new ones, but even the newest NOS ones are around 25-30 years old. One thing if it were in the trunk. Whole nuther problem because of where the factory put it. Especially in the Cutlass. PITA to fix on the car.
If the cable is broken, there will be no torque switch cutoff so the motor should run continuously until you unplug it. I've never known a power antenna motor to be quiet, so you should hear it running.
I'm no electrician here, but this is what I would do.
Power up the radio. Unplug the antenna under the hood. Check the harness wire plug for power at the plug in with a test light, or multi-meter grey for power up, green to ground. Then turn off the radio, you should get power from the down power line, from white power to green ground.
If power is available, then it's definitely in the antenna somewhere. You can repair the antenna for sure, but know what you're getting into.
Another one that has good info on how to realign the covers, etc., when doing this job. Keep in mind, your car is no Regal. The mounting bolt is not on the outer fender. It's on the INSIDE. If you've replaced yours before, then you know the nightmare ahead of you.
Now, the plastic covered metal cable is all fine and all, but will that plastic cover hold up? I dunno.
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88hurstolds here, he has, or at one time had, what I consider an even better cable and mast repair kit. What he used was some steel flex push pull cable without the need for plastic and won't fear it unraveling. He rebuilds Lightning Rods, and uses the same push cables for the buttons to detent releases as he does for the antenna. IMO, it's superior to plastic covered stranded metal cable. Regardless, ANYTHING is better than the nylon.
Something like this: