The 1841 census shows a Thomas Gawne (ref. 1463/1 19 13 Age 10 siblings Ann 4, Catherine 6, Elizabeth 2, John 13, Margaret 4 mos.
Mother Jane 40.
William turns up on the 1871 census (ref.5772 169 49 age 12 with
Mother Jane 66 and Margaret 32.
Ido not have the census so you must request someone on the board with the full censuses to check for you.
Good luck
Dorothy