I clean any dirt off the vinyl with a wet rag and NO soap. Then to further clean it and make it shine, I usually clean mine off with Murphy’s Oil Soap. It is normally used for cleaning wood surfaces, but oil soap is safe for leather and vinyl. I use about four to five capfuls and rub it in with a damp cloth. I use it for my leather seats, armrests, and vinyl dashboard and body moldings/fillers; I just wet a corner of the damp rag with oil soap. When the car is done, it looks like I used Armor All on everything. The top stays clean for about a week, and the interior (depending on how much I drive) for about two months.
You can find Murphy's (and the store brand generic) in the cleaning section of your local grocery store
You can find Murphy's (and the store brand generic) in the cleaning section of your local grocery store