The steering damper is underneath the car. I don't think it will squeak. Mine leaked the fluid out so it didn't "damp" anymore. The only effect was the steering felt "lighter". I think it is more for "feel" than anything else but people say it has some other important benefit which I don't buy, at least not on this car. I think it is not the cause of your squeak but if you want to be sure it is pretty easy to remove.

Mike

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1998 C230 330,000 miles (currently dead of second failed EIS, yours will fail too, turning you into the dealer's personal human cash machine)
1988 F150 144,000 miles (leaks all the colors of the rainbow)
Previous stars: 1981 Brava 210,000 miles, 1978 128 150,000 miles, 1977 B200 Van 175,000 miles, 1972 Vega (great, if rusty, car), 1972 Celica, 1986.5 Supra