Thomas Whitson writer here
note: I have the book 'Writers to the Signet' of 1890 and he is not mentioned.
Not all writers were Writers to the Signet.
A writer was simply a local lawyer, the kind who would now be called a solicitor.
Writers to the Signet were lawyers who were members of the Society of Writers to Her/His Majesty's Signet. Originally they were clerks or assistants to the office of the King's/Queen's Secretary. I am not entirely certain what one had to do in the 19th century (or later) in order to become eligible for membership.
I have a copy of the Register of the Society of Writers to the Signet, published in 1963. The only Whitson listed in this volume is David Shiress Whitson (10 January 1872, Edinburgh - 1 January 1932, Forfar), brother of Sir Thomas Barnby Whitson CA (10 March 1869, Edinburgh - 1 October 1948, Edinburgh), sometime Lord Provost of Edinburgh. Their father Thomas Whitson was born in Blairgowrie in 1834, so they may well be related to your Thomas who died in 1843.