If someone doesn't keep track of the sales how are they to know that a background check even took place between two private parties?
No way would I want the "government" to be the one keeping track.
As for being able to trace the firearm through its various owners, they could have the FFL that does the check issue a receipt to both the buyer and seller, but neither the FFL or "Gvmt" keeps a copy. I can't see that working very well either, as the FFL would want more than a nominal fee to do the paperwork and it would turn private citizens into archivists that would need to keep records forever. Plus it would only work for new sales via a FFL unless they required all currently existing guns in private hands be run past a FFL to get the receipt. (I would call it a form of "Private Registration".) Even then it wouldn't connect up the "Chain of Ownership" on guns already in circulation. Example: 10 years ago I bought a new gun from a FFL. 9 years ago I sold the gun at a gun show to someone. Heaven only knows where it's gone since then. Tomorrow the police show up saying that gun has been used in a crime and has been traced to me. There is no way I can see that I could prove that I no longer owned it and that I have no idea where it went. There may be a "Private Registration" receipt somewhere but it is useless as there would be no way to find it.
