I live in Bozeman, MT; about 3 hours from Great Falls. The Air Force there does not typically deploy. Their primary mission is to provide support to the missiles they have planted throughout the north central sixth of Montana (the 4th largest state in the country).
As an Active Duty Service member, this is an insult. Scammers typically try too hard to say what we say and do what we do, they ALWAYS screw it up.
I'm also originally from South Western Montana and have family up in that area. If you need to have someone check it out, I may be able to have my uncle (a Rancher and State Legislator) stop by on his way through or have one of my fellow Recruiters up there take a look at it and take pictures.
I've spent some time on that base and have never seen a Cuda on or around the compound, I can ask around and see if the guys up there have seen anything.
Alerting the Base Security to the scam may be a good idea. They may/may not be able to tell you if that vin is registered to a member of the facility (in yes or no format). I guarantee they won't provide any additional info (for security and privacy act reasons).
E-bay can also do private auctions, which must be initiated by the seller. Then you can search by the auction number provided by the seller (will also show up in your messages section). You do have to provide your email address to the seller for this.
let me know what you need and I'll try to accommodate.