(Just using this thread to hold documentation)
Here's a 2-month old Wiki page on Topeka Jack Johnson:
Topeka Jack Johnson Wiki page
I'm guessing this is advertising by the 1907 Union Giants postcard owner or his proxy, given that it does not mention the 1905 Union Giants, for which evidence exists that he did play for, but it lists the same players for the 1907 team that we were able to i.d. from the postcard. Johnson, on the other hand, does not appear to be on either of the 1907 postcards, but a 'Jack Johnson' was a star hitter for their team, as evidenced by the game description referenced on the website.
The website also states "research also list at least three players who played under the name Jack Johnson between the years of 1907 and 1939". There is nothing on the website (or anywhere else) to validate that Johnson ever played for the 1907 Union Giants - My guess is that 'Topeka Jack' was playing for the Topeka Giants in 1907 - we know that's where he was for the 1908 season and that in 1909 he was in Kansas City.
I'll have a definite answer within a few days
Here's something from the Wiki page that I did not know:
Johnson was managing his own team in 1917, called "Jack Johnson's Topeka Giants" who played the All Nations base ball club.[3]
Edited to clarify 1907 reference above