The Barrack Department was a separate department that looked after the barracks. So different to the Regular army and the Militia. They employed Barrack Masters - who are listed in the annual army lists; Barrack Sergeants, who like William Duke were almost always Ex-NCOs discharged to pension. These are listed in entry books in the National Archives, which I will try and find later
They also had Barrack Labourers who only seem to be listed in census.
Ken