There are several HOMER wills from the Birmingham and Dudley areas. There is one for a Samuel (1832?), but no place is given. There is also at least one from Cradley, which is near Rowley Regis and is also where some of the people I listed from the 1841 census are living by 1851.
Note that Rowley Regis was Staffordshire, but Birmingham also covvered parts of Worcestershire and Warwickshire.
Wills are downloadable for, I think, £3.70, so are at least something you can check out from a distance, even if only to eliminate.