On Strips: The Original Comic Strip Inking Guide?
While Art Instruction, Inc. was founded back in 1914, it was originally just a general illustration school. What I came across recently was this book from the 1930s: Comic Strip Magic Drawing Book. (There's no copyright information available, but the "No. 861" corresponds with other numbered books from the publisher from around that time.) From the box cover, it appears to be a how-to manual for drawing your own comic strips.
However, once you remove the lid and open the book, what you find is a series of four-panel comic strips already drawn and lettered. The first three panels of each strip are essentially complete and the fourth (much larger) panel is printed very lightly so that the reader can trace or ink of the existing lines to complete the strip.
The quality of illustration isn't bad, but the storytelling and "jokes" are. In fact, of the pages I've seen (I don't own this) the "plots" all center around an animal discovering an object they would like to obtain, only to discover it's false or they've made a mistake. (The fox thinks a feater duster is a rooster's tail, for example.)
Regardless of the quality, this is the earliest instance I've ever seen of a commercial enterprise singling out inking as a separate and distinct discipline than penciling. The Eisner-Iger Shop -- which famously broke down the comic making process into the typical duties we see today -- opened in 1936, and since we don't have a firm date on this book, it's possible it did come out later, but that numbering implies the first half of the 1930s.
So this could be the first instruction book on comic inking?