The image (perhaps based on a half-length portrait of Darby painted by Sir William Beechley in 1801 and later sold as an engraving) wears a Nile medal – a reference to the Battle of the Nile in 1798 where Darby had command of HMS Bellerophon.
Some 49 Bellerophon crewmen were killed and 148 wounded during the battle with Darby himself rendered unconscious with a head wound.
Tennants estimated the 3 x 2½in (8 x 7cm) watercolour on ivory at a conservative £300-400 but bidding reached £5200 at the auction on January 11.
A late-19th century Damascus cabinet was one of nearly 400 lots of furniture, artefacts and works of art collected by Midlands dealer AT Dexter on his 30 years of travel throughout the Middle East and India.
The collection was offered at Tennants on January 18.
Standing 4ft 11in (1.45m) tall, the hardwood cabinet with an arrangement of cupboards, drawers and mihrab niches is inlaid throughout with mother-of-pearl and bone.
It sold to a northern English dealer at a double-estimate £1300.