Hello,
Below are two links that have a capsule history from "Tennesseans in the Civil War, Volume 1."
Ashby's 2nd Tennessee was made up of the 4th and 5th Tennessee Cavalry Battalions. One of my ancestors was in Company H (Ashby's) 2nd Tennessee Cavalry.
http://www.tngenweb.org/civilwar/csacav/csabrann.html
http://www.tngenweb.org/civilwar/csacav/csaashby.html
Your ancestor was in Company G (Ashby's) 2nd Tennessee Cavalry. That company was from Monroe County. Organized at Sweetwater on 28 June 1861.
From what I can tell, he nor his widow filed for a Tennessee State Soldier's or Widow's Indigent Pension Request.
Your will need to check his Compiled Military Service Record for further information (that is the stuff you obtain from the National Archives). If you are located in the state of Tennessee you can obtain it from the Chattanooga Public Library, the Tennesse State Library and Archives, or the Eastern Tennessee Historical Society for much less than the National Archives.
Please let me know if you have any questions.
Respectfully,
Gerald D. Hodge, Jr.
War Between the States Historian
Historian: 39th Georgia Volunteer Infantry Regiment
http://39thgavolinfrgt.homestead.com/39thHomepage.html