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I agree that it could be the crank position sensor, as it supplies the RPM signal for the engine (possibly causing the studder) and also provides the RPM signal for the Tach. This is assuming, that since you have the Grand Prix GT, that it has the 3800 engine. Crank sensors are very common on the 3800 engine. Usually, the sensor will set a P0336 or similar fault code, which may be why the light is on.
To be sure, I would reccomend you get the codes scanned, but if you would just like to know the most likely, I agree with the Crank Position Sensor.
Please let me know if you have additional questions!