A biography of David Hume says
David Hume left the University of Edinburgh around 1733. Hume chose the job as a stool in a merchant's office in Bristol.
What is a stool?
Here's the reference to the biography in question.
The full sentence reads:
The careers open to a poor Scottish gentleman in those days were very few; and, as Hume's option lay between a travelling tutorship and a stool in a merchant's office, he chose the latter.
In this case a stool refers to "a single seat on legs or a pedestal and without arms or a back." link
A "stool" is not a job description, but a physical description of where he sat, in order to contrast it with the other option of a "travelling tutorship"
Your confusion is understandable, as, later in this book, there is a reference to a "Chair", which is a job title in academia.
In 1744, Hume's friends had endeavoured to procure his nomination to the Chair of "Ethics and pneumatic philosophy"...link
Which refers to Definition #3, here "a professorship."
Stool can also be used to describe a 'spy' or 'informer' in the enemy's camp, be it in politics or business.