It’s unclear if this William is a son of James Hamilton Sr. and Jane Allison or not although he is the right generation, lived in Harbourville and was born in Ireland. A William Hamilton is listed in the 1851 censuses in the same voting district of Somerset as James Sr., James Jr.
and David. Land deeds show land at Bay Shore sold by James and Jane to William Hamilton in 1861. His location is shown at the west wharf waterfront in Harbourville on a map from 1864. He’s listed by himself with no family in the 1871 and 1881 censuses in Harbourville where he was a Sea Captain and then 1891 and 1901 censuses as a lodger in Kingsport.101
The difficulty lies in that his birthdate seems to be within a few months of his “sister” Sarah so perhaps he is not a sibling after all...