Hostgator uses eNom for domain registrations. A good place to look for it would be at eNom's ClubDrop.com. Enom also put expiring names at SnapNames.com. So they would be the best places to backorder it.
I should mention that Hostgator isn't the registrar but the webhost. You need to do a whois lookup at iWhois.com to know who the actual registrar is without guessing. If it's not eNom then let us know who it is and we can advise further.