Should first point out for clarity that the year of the directories is the year of publication, and the date of the survey from which the information is based is usually taken as the year before the publication year.
That said from other directories:
1903. No Joseph Griffin listed.
1904. Joseph Griffin, Eagle & Ball PH. 12 Penn St
1908, 1910 Joseph Griffin beerseller. 41 Trevor St, Nechells
1921, No Joseph Griffin listed.
The term beerseller means that it was either a beerhouse, which had a licence only to sell beer and cider on the premises (and was probably a small pub), or an off- licence , which could only sell alcohol for consumption off the premises. The Eagle & Ball, by comparison was a full scale pub,. so a bit of a come-down from the Eagle & Ball to a beerhouse.
A photo of the Eagle & Ball, which more recently was known as Moby Dicks (Ugh) is below
There is also a John C. Griffin , beerseller at various addresses in Balsall Heath at this time. Could he be related?