The following obituary is a bit strange if he was mayor.
The Caledonian Mercury of 23 June 1806 carried it, it was a fulsome tribute to 'James Sempill, Esq. M.D.' who died 'at an advanced age' in his house in the Mall, Waterford, it confirms that he was 'father-in-law to our much respected countryman, John Anderson, Esq. of Fermoy' and describes James as 'one of the Aldermen of the Corporation of Waterford' (I think the Alderman references in this topic so far have been to Alderman of Limerick?). There are bits of glowing testimony about his life, which the inhabitants of Waterford witnessed 'for upwards of 40 years'.
But it doesn't mention that he was mayor.