Today, I thought I might speed things up and show you a couple sets. Both of these can be linked to sets listed in Engel's most recent guide, though neither set indicates the existence of non-sport cards.
As always, it's possible that baseball and non-sport cards were issued together, or sold separately but were issued at or around the same time.
I think it's important to note that backs might have been "recycled" from card set to card set. And a series of card backs or even entire card sets might have been sold to various printers to use, at least in the 1970s as menko cards were losing popularity to Calbee and Bikkuriman. Dates here are based on Engel's guide for baseball card sets; these sets were probably produced around the same time.