[Mr70]

I too am an advocate against auctions w/hidden bidders,as well as those w/their feedback being hidden too.I avoid them like the plague as they do more harm then good IMO.
If the argument for private auctions is because bidders will get a bogus Ebay Second Chance Offer emailed to them afterwards,they can easily verify if that Second Chance Offer is authentic by simply clicking on their "MY EBAY" page,then scroll on the far left column to the "MESSAGES" button showing messages received through Ebay.
If it is indeed a real authentic Ebay approved Second Chance Offer,the bidder will see that EXACT same Ebay email offer listed there too.
I would opt for a non private auction,especially on something as large,expensive and as serious as an automobile.