The one bought from the dealer may come back with a DROS record. The AFS system came into place in the mid 70's and paper DROS forms mailed to DOJ by the dealer were manually inputted into the system. There is a chance the one from the 60's may have a DROS record to the original purchaser, but more than likely there will be no record.
Until 1992, transfers between private persons did not require the use of an FFL or any paperwork.
You can always submit a VolReg form which will generate a record similar to a DROS record in AFS. There are pros and cons to the VolReg. Many people want to be "of the grid" while others prefer a record in AFS to verify ownership.
If you are caught illegally carrying a concealed handgun, and there is no ownership record in your name, the offense may be prosecuted as a felony.
If You Heard The Shot, You Weren't The Target