I tried a few different cleaners today, and the only thing that worked was carb cleaner! It took a while, and I had to keep using new towels because they were turning completely black. But there is actually hard clean plastic underneath. Could it be 20 years worth of neglect? The car isn't spotless, but there certainly wasn't this level of buildup elsewhere.

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1985 380SE Blue/Blue - 230,000 miles
2012 Subaru Forester 5-speed
2005 Toyota Sienna
2004 Chrysler Sebring convertible
1999 Toyota Tacoma