Below is the extract from "Tennesseeans in the Civil War, Volume 1" that is a capsule history of the regiment.
Also, the book "The Old Nineteenth Tennessee Regiment, C.S.A." by Dr. W.J. Worsham [chief musician of the regiment] is available. The manuscript for this book has a whole lot of additional information than the published book and is either in the Eastern Tennessee Historical Society Archives or at the University of Tennessee.
Dr. John Derrick Fowler did his doctrinal dissertation on the regiment and I believe still teaches at the University of Tennessee in the Department of History. You may want to attempt to contact him and see if he has any additional information.
You really need to look at your ancestor's Compiled Military Service Records to get an idea if he was present during Shiloh. The records are available at the Tennessee State Library and Archives, Chattanooga Public Library, and the Eastern Tennessee Historical Society.
My wife's ancestor was in this regiment in Company F.
I hope this helps.
Gerald D. Hodge, Jr.
War Between the States Historian
Historian: 39th Georgia Volunteer Infantry Regiment