Here is a solution for the common problem known as sticky parts of ferraris.
This is something you can do at home. I'm not recommending brake fluid or any other pro. chemical products.
I used a cheap perfume to loosen the rubber layered on the sticky part.
This part usually doesn't get sticky. But I had a metal keyring and it scratched all the rubber around the ignition place. so It needed to be fixed.
1) We need a cheap perfume and a small piece of soft sponge. (don't use sharp sponge at all! it can scratch or make holograms on the part)
2) Sprat it on the part and wait 3-4 minutes for it too get loose.
Spray 10-20 times in the small sponge. make it all wet with the perfume so sponge will solve and absorb the rubber like black water.
3) You can do 2nd finishing with a cloth like microfiber to absorb it all and you'll have all- clean plastic.
Use some napkins, spray on the part and rub the napkins. the tissue slighly get black and dirty and that's the final remaining layers of rubber.
4) This step is not mandatory, but I sprayed some Hydrating solution. It will not be like wd40 to make it oily funny. It works like you have a brand new plastic and removes the shine and you'll have a fresh plastic part.
*But it is not necessary...
** You also can use leather sprays.
5) Fix it back.
The cover is so easy to open and close, just make sure pulling the steering well out and up first.
I already explained how to clean ashtray and door handles in this forum.
Goodluck , and ask me if you have questions.