1850 Census: Oktibbeha [County], Miss.: he is a 16 year old student in the household of Mrs Margaret Ware; with Margaret and Thomas are John Ware? (23) and Jane Ware (19) as well as Thomas Adams (26), overseer. On the slave schedule, a Margaret Ware is listed with 12 slaves (ranging from 3 yrs. to 50)
1860 Census: cannot find him-if he did, indeed, serve in Alabama, that is where he may be.
1870 Census: Police Beat 5, Oktibbeha [County], Miss. He is a 37 year old farm laborer with Elizabeth (39), William (15), Thos. Jr. (11), Robert (3 or 5) and Joseph (2)
1880 Census: Webster, Winston [County], Miss. He is a farmer with wife, Elizabeth and 8 sons & daughters.
According to the censuses, he was born in South Carolina.
Find a Grave:
https://www.findagrave.com/memorial/103615702/thomas-f-ware
There is information added but the gravestone record says that he was born Oct. 4, 1834 and that he died Jan 8, 1893 [only 1 day off from the grave registration [post #2, above].
I was unable to find him on HDS.