Auctions are not a hands-off selling platform. The seller still needs to provide an informational package, documentation, pictures, and transport for the car. Many auctions require the seller be present during auction and most charge to run a car through auction regardless of sale or not.
Selling a car isn't rocket science. Clean the car, take good pictures, advertise at a reasonable price, and wait. Get a Marti report. If it's as nice as described, it will sell. Don't rule out the free sites.
Hemmings = $100-170
Autotrader Classics = $50-150
BAT = $100
eBay = $125
Craigslist = free
KSL = free
Mustang clubs = free