Dear Mr. O’Toole,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located Carded Records Showing Military Service of Soldiers Who Fought in Confederate Organizations , 1903 - 1927 in the War Department Collection of Confederate Records (Record Group 109). Portions of this series have been digitized and are available online using the Catalog. We searched the series for soldiers from Tennessee with the last name of Graves and located 190 records, however none of them had the first name of “Willis” given in the records. Some had their first names indicated only by the initial W, however all of these had a middle initial other than N.
We also searched the copies of the records available on Fold3 but were unable to locate a definite match.
Finally, we searched the National Park Service Civil War Soldiers and Sailors System (CWSS) and located only results for "Graves, Willis" for Union soldiers. We did find results for “Graves, W.” that served in the Confederacy but none of these were from Tennessee units.
Please keep in mind that due to the circumstances of the war, not all Confederate records survived the conflict, and not all CSA records that did survive ended up in federal custody. The Tennessee State Library and Archives may have additional information about soldiers and units from their state that fought in the Civil War.
We hope this information is helpful. Best of luck with your family research!