Having owned/showed a '56 Chevy post with a 20 yr. old white rolled and pleated naugahyde interior, and having worked as a detailer in a used car lot in another life, I can give you a little experienced advice.
When we first got the '56, I used a good all-purpose cleaner to cut oil, grease, and dirt (Spic & Span, 409, Mr. Clean) with a soft short-bristled brush to get in the cracks & crevices--not too heavy on the water when rinsing. I used Shaklee products like Basic H, Basic I, and At Ease (a cleaner with a little abrasive) for the badly discolored areas. Use a soft, absorbent cloth to remove the dirty residue.
The maroon shouldn't really retain many stains. I once used this method to clean the red vinyl back seat of a '64 Falcon whose previous owner owned a large farm dog that always rode in the back seat. Except for the toenail scratches, the seat came out immaculately clean.
Thorough cleaning may open the pores of the vinyl, so you need something to protect it after it is cleaned. Otherwise, you'll be recleaning in a short time and the seat will look dull.
DO NOT use Armorall or like products, especially if you ever plan on painting anything within two counties of your seat. If you do used these products, plan on fighting fish eye in your paint forever. There is a product called Poly-Crackerthat is used to clean surfaces to try to overcome the problem but...........plan on paying the price in extra time spent cleaning before priming and painting. And that's a whole other story!
Any of the heavier creams for vinyl, plastic, and leather items should do just fine to protect the seat as long as the product dries to a hard/shiny finish.
Good luck.