As I understand it:
- if the clubs were originally bought "off the rack" (ie not customized by Titleist), then only the 6-iron would have a serial number.
- if the clubs were built by Titleist via custom order, then all of the clubs in that custom order would have the same serial number (ie it would track back to the order ticket internally at Titleist).
Serial numbers don't always tell authenticity. Counterfeiters have also been known to etch fake serial numbers onto clubs to fake authenticity.
2nd Swing has been around for quite a while, I doubt they would sell counterfeits. After this COVID thing is over, a phone call to Titleist could probably give you the set's history (ie specs, original shafts, grips, etc.)