Almost all the information I have so far on the Gee families of NH/VT is from Mike Gee's website (http://www2.arkansas.net/~mgee/index.html - email address: email@example.com). He cites the source of information as 'Decendants of Solomon Gee of Lyme, Connecticut' compiled by Charles E Benjamin1981, Library of Congress Number 81-81764, printed by Light and Life Press Winona Lake, Indiana.
The Solomon Gee born 1817/18 you asked about looks to have been the son of Solomon and Rachel (Hartshorn) Gee. They married 19 Aug 1804 at Lunenburg VT and had a son Solomon born 14 Oct 1818, died 23 Oct 1872 - his wife and children not listed. Solomon (Sr.) was the son of Leuman and Betty Cate (Bruce) Gee according to the gedcom at Mike Gee's website (I haven't seen the actual BOOK, so I can't vouch for any typos which may be in the gedcom, if any). Hopefully Mike Gee may have further info for you, or Virgil Huntley, who very kindly replied to my original message, may know more. Hope this helps. Regards, Scott Ives