I have been a detailer for 18 years and most pro shops use an all purpose type cleaner. Look at you local auto parts store for some thing made for interiors and make sure it says it is ok for use on vinyl. Stay away from products like 409 they are too strong and can strip color and all sorts of things which is bad news.The best way to clean vinyl is like this:
1. Make sure you have a bucket of mild soapy water(Car wash soap is ok), a wash mit, a medium stiff nylon brush, the all purpose cleaner, and some clean dry towels.
2.Wipe the panel or seat from bottom to top with the wash mit first to get things wet, the reason for this is to keep the all purpose cleaner from streaking or making marks on the vinyl. It also helps delute the cleaner more evenly over the surface.
3. Spray the all purpose over the panel from bottom to top and scrub it with the brush, then towel dry the panel or seat. If you have an air compressor you can blow all the cracks and crevises out to get the dirt from under them which which really helps, especially in seams and around threaded work in seats.
4.When you are done use your favorite vinyl protectent as usual, This will help the next time you need to clean your vinyl and it will also help repell future dirt and stains. I hope this helps you if you have any problems let me know I always want to help whenever possible
5. As for the chrome the steel wool idea is your best bet. Glass cleaner is great, If you have any thing like road tar,paint over spray etc, a little lacquer thinner on the steel wool works good but be careful of all other surfaces.
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