I don’t know if these are helpful (where no directory listed it is Kellys):. I have included all Goodyears listed in the commercial section, though some may have no connection, and have gone up to 1913. I think the baker William Henry must be different to yours, but there might be a connection. You will see William Henry is listed briefly in 1910 as a boatbuilder, and a William appears again as one briefly in 1903:
Whites 1848: Goodyear David, timber dealer, Oozells st.,North ; home:14, Cumberland st
Slaters 1852: Goodyear David, sawyer Mill St
Whites 1855: : Goodyear David, English timber dealer, 4,Oozells street
Dix’s 1858 : Goodyear David, boatbuilder, Icknield port rd; home, Freeth st
David is not listed in the 1862 corporation directory, but there is a George Goodyear, , brass tube maker, Icknield Port Road- though there may be no connection
Corporation 1862 : Goodyear, Thomas, sawyer, 6 Scotland St, Parade.
1868: Goodyear,Edward & William, boat builders, 5 Kingston Road.
1868: Goodyear, Samuel, shoemaker, 26 Ingleby St
1872 : Goodyear Thomas, boat builder, Plume street
1872 Goodyear Wm. boat builder, Canal bank, Sandy la. Camp hill
1873-83: Goodyear Edwin, timber dlr. Charles Henry st
Whites 1873: Goodyear George, shopkeeper, 219 Icknield Port road
Whites 1873: Goodyear Thomas, boat builder, Plume street ; home Vale
Place. Beales street. Aston
Whites 1873: Goodyear William Henry, boat builder, Croyden villa,
Golden Hillock road
1876-1905: Goodyear Thomas, boat builder, 53 Plume street (number Plume st only listed after 1897)
1876-78: Goodyear Wm. boat builder, Canal bank, Sandy la. Camp hill
1876: Goodyear William Henry, baker, 31 Dudley road
1878: Goodyear William Henry, baker, Grove Lane Smethwick
1878-80 Goodyear,Esther ( Mrs), dressmaker, 35 Barford Street South
1879-80: Goodyear William Henry, baker, Grove Lane Smethwick & 129 Spring Hill
1882-92: Goodyear William Henry, baker, 169 Grove Lane Smethwick
1884-92 : Goodyear Edwin, timber dlr, 428 Moseley Road
1888-92: Goodyear,Esther ( Mrs), dressmaker 1 Varna road
1895-99: Goodyear Edwin, timber merchant, 152 Moseley Road (this is the same place as earlier, but street renumbered.)(In 1900 it seems to have been taken over by George Shipway, timber merchant)
1895-96 Goodyear, joseph, butcher, 35 Gt Russell St & 23 Summer Lane
1895-99 Goodyear William Henry, baker & confectioner , 3 Cape hill & 206 Windmill Lane
1897 Goodyear, Joseph, butcher, 35 Gt Russell St
1897-1900 Goodyear, Lucy (Mrs) dressmaker, 35 Ladywood Road
1899-1900 Goodyear & Parker, Drapers,30 Lincoln St,,Balsall Heath
1899-1900 Goodyear, Mary Ann (Mrs), Kings Head PH, 73 Bell Barn road
1900-13 Goodyear, Alice Maud (Miss) , milliner, 178 Stratford rd
1900-08 Goodyear William Henry, baker & confectioner , 3 & 104 Cape hill & 206 Windmill Lane & 372 Dudley Road.
1903-04 Goodyear. George, hairdresser, 181 Corporation st
1903 Goodyear, (Mrs). Dressmaker, Ladywood Grove, Ladywood road.
1903 Goodyear, William, boatbuilder, Brittania wharf, Watery Lane
1910-13: Goodyear Charles, dining rooms, 62 Dudley road
1910-13: Goodyear William Henry, baker, 528 Bearwood road ; 32 Cape hill & 206 Windmill lane, Smethwick
1910: Goodyear William Henry, boat builder, Blcws street
Mike