Since the Mikimoto employee I spoke to said silver might be marked with an S, and your family history is that the clasp is silver, I would think the clasp is silver, despite what the eBay sellers you refer to may claim.
I suppose you could test it with the appropriate acid, if you are in doubt. (But why?)
Take this listing, for example...to me that looks like a silver clasp that has the typical patina that silver develops from oxidation (tarnish.)
https://www.ebay.com/itm/Mikimoto-P...077376?hash=item41d659b480:g:ygEAAOSw5UZY~5Eb
Perhaps the seller hopes to make more money by claiming that S stands for platinum...
Now take this listing:
https://www.ebay.com/itm/Lovely-MIK...695245?hash=item2f0fb09b4d:g:jl0AAOSww9xZDWtu
Even though the username is different, it has to be the same seller-- see the item location? Both this one and the other listing are located in Rapid City, South Dakota. So it's just one seller making this claim, not two. The two usernames both end in 4u, also.
Incidentally, I scoured the Mikimoto website, and nowhere does it state that S means platinum. I think that seller is blowing smoke.