In
Arms Makers of Maryland by Daniel D. Hartzler and published by George Shumway, is a detailed family tree of "Hawken Family of Gunsmiths". The family tree was compiled by George Shumway and Glen R. Scott & Juanita M. Scott. Juanita Scott is descended from John Hawken of Hagerstown, a son of Christian Hawken, Sr. At the time the book was published, the researchers had found fifteen members of the Hawken family that were gunsmiths.
As others have mentioned, Jacob and Samuel had a brother named William that was a gunsmith. He took over his father's gunshop in Hagerstown when the father died. Several rifles are known with "W. HAWKEN" marked on the barrel and are thought to have been made by William Hawken of Hagerstown.
There was another branch of the Hawken family that was in Springfield, Ohio. These likely were descendants of Nicholas Hawken, brother of Christian, Sr. A Henry Hawken died in Springfield, Ohio on April 15, 1835. He appears to have moved to Ohio around 1815 from Westmoreland County, PA. His connection to the Hagerstown Hawken family is not well documented, but family tradition has Hagerstown as their place of origin. Henry Hawken was a gunsmith and may have been a son of Nicholas Hawken. Henry Hawken had at least two sons that were gunsmiths, John Hawken and Daniel Turney Hawken. Several rifles are known with "D. T. HAWKEN" marked on the barrel and a few with "H. HAWKEN" and "J. HAWKEN". Jim Gordon has one of each in his collection and published pictures of them in his book
Great Gunmakers for the Early West.
Gordon also has in his collection several rifles marked "W. HAWKEN", one marked "C. HAWKEN", one marked "C. & J. HAWKEN" and one marked "S. HAWKEN". All these rifles are of the Hagerstown school in architecture and mounts and thought to be the products of Christian, Sr., and sons Jacob, Samuel, and William. Below is a picture of these rifles.
The top three are marked "W. HAWKEN". The fourth one down is marked "C. & J. HAWKEN". The fifth one down is marked "S. HAWKEN". It should be noted that the "W. HAWKEN" marks are stamped in block letters. The "C. & J. HAWKEN" and "S. HAWKEN" are engraved in script.
The subject rifle is very similar to these five rifles.
Interestingly, the patch box on the subject rifle is most like the ones on the "C. & J. HAWKEN" and "S. HAWKEN" rifles shown below.
The engraved eagle inlay on the cheekpiece of the subject rifle is very similar to one on the "C. & J. HAWKEN" marked rifle.
The auction site doesn't show a photo of the "HAWKEN" name on the barrel of the gun, and the description doesn't say whether the name is engraved in script or stamped in block letters. That information might help in attributing the rifle to one of the brothers.
With the meager info on the auction site, I might lean towards either Jacob or Samuel as maker of subject rifle, but William is still a possibility.