Maybe im a class 8 retard (I am) but my understanding of firearms is that you can use the serial number to trace its EXACT providence. was it defaced? My thinking is that leaving the firearm behind means a level of obfuscation has taken place that can usually only be attributed to state actors.
You're not entirely retarded, but the serial would only be able to trace which FFLs it's been transferred to. In the situation of a normal gun store purchase, or a mail order purchase, you would have records of it.
However, in the case of a private transfer, like for a craigslist/armslist type sale, or if he inherited it or received it as a gift from someone, the serial would only be able to track it to the last time it was trasferred by an FFL.
If that were the case, you'd just have to hope that the private seller retained accurate records.
Only the receiver of the gun is is required to be serialized, and that receiver may have been manufactured in the 1930s.
I think many people are getting hung up on the "mauser" bit (thinking that it must be a k98 or something), but it must be noted that the mauser action is pretty ubiquitous in modern sporting rifles. It's a pleasant to operate action that's both strong and easy to manufacture, so basically everyone uses it now for modern guns. Everything from the Ruger American to the Mossberg patriot uses a mauser type action.
To me, the firearm everyone is looking at appears to be a modern sporting rifle, and guns like this are rather cheap ($200-$300), which would fit with a fairly young man buying it.