Roster of South Carolina Patriots in the American Revolution, page 856, lists Thomas Shannon as having served 213 days as a horseman in the Militia in 1781 & 1782, in the Company of Col Richard Winn, commanded by Col William Hill. At some point he was made a Captain. In doing research, the name Capt. Thomas Shannon comes up many times in the Pension Applications of other Revolutionary War Soldiers, as having riden with the Captain, on patrol in search of Tories. I do not find any Pay/Muster cards or Muster Rolls with his name on them.
Per the Daughters of the American Revolution Genealogical web site:
SHANNON, THOMAS Ancestor #: A102843
Service: SOUTH CAROLINA Rank: CAPTAIN Birth: 1735
Death: (ANTE) 12-14-1812 FAIRFIELD DIST SOUTH CAROLINA
Service Description: 1) COLS RICHARD WINN,COL. WILLIAM HILL, MILITIA
ROSTER OF SC PATRIOTS IN THE AMERICAN REVOLUTION, MOSS, P.856
Residence: County: CAMDEN DIST - State: SOUTH CAROLINA
Spouse: Elizabeth Taylor...Col. William Hill, of S.C., was at King's Mountain, see Moss's book 'The Patriots of Kings Mountain,' page 122.