I wouldn't use anything. A lot of products dry out the materials, and since it's a vinyl type of material, it's not really going to absorb anything that could prolong it's life like a leather material would.
I've been using the 303 Protectant (Thanks Paul Shinn for the tip) top, running boards & tires. I've been very happy with it. It doesn't leave a shiny greasy feeling behind.
The originals were a pyroxylin coated fabric that resembles vinyl. Vinyl didn't show up till the 1950s. Pyroxylin is a form of cellulose nitrate much like the dope that was used on the old rag wing aircraft that used grade A cotton fabric and nitrocellulose dope with aluminum pigment added to the final coats before the color coats are sprayed on. This stuff doesn't like a lot of sun light since it deteriorates rapidly in sunlight. If still intact then it can be cared for much like the old aircraft of similar material but the older it gets, the more complicated the care can be.
Joy liquid detergent has been used as one of the mild detergents to clean rag wing aircraft. It cuts the crud well but is mild enough not to do any damage. Using soft washable towels and a spray bottle with joy and water is a good way to clean the surface followed by a damp rag and soft dry rag wipe. Carnauba wax shouldn't hurt a well cared for surface if gently applied. This type of wax can be removed more easily when washing so it doesn't build up like some do. If the surface is cracking or getting in poor condition then it will need other processes to clean and protect it further. I would avoid anything with silicone as a protectant. It just doesn't seem to work well with older style materials. It doesn't do vinyl much good either.
303 Protectant is a proprietary material that is water based. They won't tell a person what's all in it but at least they tell you what is NOT in it. It is listed to have no harmful silicone oils but it has siloxane emulsion for water proofing so it does have a form of silicone in it. How it would effect pyroxylin is unknown but it may be a risk. The 303 would likely be OK for a vinyl fabric but I can't say that with certainty either.
Griot's products are spectacular! Been using them for years on my Model A's Interior and exterior! No residue! Waxes etc are superb! Go on line and Amazon now carries some of their products! Your choice
Ditto using 303 Protectant on the vinyl top and it also works great on tires. 303 Protectant dissolves the yellow tinge that exudes from new tires. It also does a nice job of cleaning brake dust of of light colored Model "A" wheels. Put it on the running boards also.