It does not appear that your Tom Tucker served initially in the 14th SC. Note, his tombstone only records the 14th from which he was discharged for wounds January 1862.
The 7th SC Cavalry appears to be composed of a potpourri of organizations. I do not find a T. Tucker in any of the identified units.
......
Thomas M. Tucker, 2nd Corporal, Company I, 14th South Carolina Infantry, enlisted September 3, 1861 at Camp Butler, S. C. by Capt. H. H. Harper, was wounded, no date listed, discharged on Surgeon’s Certificate of Disability January 1, 1862, 24 year old Farmer, born in Abbeville Dist., S. C., 5’ 11”, Dark complexion, Glue eyes, Dark hair
Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of South Carolina
…………
Corp Thomas Moseley Tucker
Birth: 1836, USA
Death: Oct., 1911
Lowndesville
Abbeville County
South Carolina, USA
Thomas Moseley Tucker was wounded in the War between the States, having served in Co I, 14th Regiment, CSA
Find A Grave Memorial# 52033585
………..
The 7th Regiment South Carolina Cavalry was organized during the period of March 18, 1864 through May 1864 by consolidating five independent cavalry companies: two companies of Tucker's Squadron, one company of Boykin's Squadron of Mounted Riflemen, and the 2nd Company of Trenholm's Squadron (two companies). Also involved in the organization was the cavalry battalion of the Holcombe Legion which contained 5 companies (another source says that two companies of Rutledge's Squadron of Mounted Rifles was also involved).
https://familysearch.org/wiki/en/7th_Regiment,_South_Carolina_Cavalry
See also: https://sites.google.com/site/companyf7thregimentsccavalry/home