Greg, I thought I told you:
never joke about 100+ year old pennants!
Okay, you got me ... thought maybe you missed the connection; and, I was gonna totally make your day.
Cool pennant. Seems to be manufactured by the same mystery maker as this ca. 1916 Brooklyn Robins (Dodgers) pennant. Artwork is very similar, down to the charcoal shading used on the uniforms; and the coloring of the shadows between the players' legs.
Which means the Dodgers and Giants, in this mystery artist's view, wore identical unis back then....