It appears that the earliest reference to "false dealing"of any type is in the Liber Vagatorum which was published ~ 1509.
The earliest actual reference to mention the second deal (no explanation) is in the OPERA NUOUA DOUE FACILMENTE POTRAI IMPARARE PIU GIUOCHI DI MANO ET ALTRI GIUOCHI PIACEUOLISSIMI & GENTILI COME SI POTRA LEGGENDO UEDERE ET FACILMENTE IMPARARE. This four-page pamphlet was published by G. S. di Carlo da Pavia in approximately 1520. We don't know if he was writing about the strike or push-off, as no real details are given.
You also find mentions of the move (but no explanations) in How Gamblers Win: or the Secrets of Advantage Playing (1865) by Gerritt. M. Evans. It's not entirely clear that Evans was talking about the strike second per se, but the language he uses in describing the second makes that theory seem likely.
Quinn's Fools of Fortune (1890) is a possible early candidate for the strike second deal, as pointed out by Darwin Ortiz in The Annotated Erdnase.
References can also be found in Koschitz's Manual of Useful Information (1894), Hardison's Poker (1914), and Poker to Win by Al Smith, which was apparently written in the early 1930s although perhaps not published until much later. Both the Hardison and the Al Smith books are clearly talking about the strike second deal. Koschitz uses language that suggests he is talking about the strike, but it's possible he was referring to the push-off.
One or two other references can be found in Poker: It's Laws and Principles (1915) by Algernon Crofton. As is typical, it can't be precisely determined if he's referring to the strike or push-off, but he mentions the "swishing sound" made by the deal which is more common with the strike.
Additionally, there is an article in Scientific American magazine from the early 1920s that mentions the second deal.
But, the earliest known description of the strike second deal comes to us from Dr. James Elliot. He published his method of doing the strike from the long edge of the deck in Mahatma magazine in 1898. The top card is pulled back (instead of pushed over) and the right thumb strikes the second card at the long edge just above center. Granted, this isn't the modern strike second deal that we think of today, but it is a strike.
For the modern form where the thumb makes contact at the upper right corner, the Hardison reference is probably the earliest known souce.
Once you get into the magic literature, you can turn to the original Walter Scott Phantom of the Card Table (~ 1930s) manuscript, ...And a Pack of Cards (1927) by Jack Merlin, The Card Expert (1938) by Lynn Searles, and Expert Card Technique (1940).
Hope this helps.
Jason