His elder brother, William Hamilton, succeeded their father but died unmarried before November 1703, after which the Baldoon estate passed to Basil.
[2] During the Jacobite rising of 1715 he commanded a troop of horse under Thomas Forster and was taken prisoner at the Battle of Preston.
He was sentenced to death in 1716, but reprieved through the influence of his uncle Lord Orkney.
His estates were forfeited, but successfully claimed by his mother, and the forfeiture was reversed in 1733.
[1] In 1734, he unsuccessfully stood as the Duke of Buccleuch's candidate for Dumfries Burghs.