The style of the illustration, the lettering, the use of "Pep" - twenties all the way. Wikipedia:

Moe noticed that many successful West Coast businesses used their owners' first names. One he liked in particular was a dress shop called Minnie, Maude and Mabel's. As soon as he returned to Philadelphia, the store's name was officially changed to "The Pep Boys — Manny, Moe & Jack".

Shortly thereafter they commissioned the Manny, Moe and Jack caricatures that still serve as the company's logo. When Jackson left in 1925, his caricature was replaced with that of Moe's brother, Isaac (Izzy) Strauss. (The company name remained the same despite the personnel change.)

So that's not Jack on the end?

No further changes were made to the logo until 1990, when Manny's cigar was removed.

Of course it was.