I get spots like these on the white vinyl seats on our boat. In this case, the spot are droppings from small spiders that hang out under the canvas. Scrubbing with a cotton rag and my usual general purpose boat cleaner (Blue Coral Car Wash) will get rid of the spots completely, unless the spot has been there for several weeks. If the spot has been there a long time, some yellow discoloration may remain on the the vinyl. I suspect that is the result of a chemical reaction. Sometimes the sun will fade it away.
I haven't used any of the specialized vinyl cleaners, but they are around and you'll be hearing from ROs that use them.