Judson Brown invented what is clearly the basis for this classic trick. Brown's inspiration was a prepared deck that could make any card chosen disappear: Eric Impey's “Mysto, the Masterpiece” in his manuscript Original Card Mysteries, 1928. Using Impey's idea of using waxed-together pairs of cards, Brown adapted it to make any card named turn face up in the deck: “A Super-Reverse Problem” in The Sphinx, Vol. 28 No. 1, Mar. 1929, p. 25.

Dai Vernon's “Brain Wave Deck” was originally published in The Jinx, No. 49, Oct. 1938, p. 341. The first sentence holds a long-overlooked truth: “Eight years ago, in 1930, I evolved what was a new effect in subtle cardology.” The key word here is “evolved”, which likely acknowledges Judson Brown's “Super-Reverse Problem”. John Crimmins, Jr., in a footnote to the “The Brain Wave Deck” published in Annemann's Practical Mental Effects, 1944, p. 251, gives this history: “Subsequently Dai Vernon was working with the same principle [waxed pairs] and really popularized the deck. In his version, he used beeswax to hold the pairs together, and treated each card on its back so that he worked with a face up deck. Needless to say, the finesse with which he handled the deck, soon elevated the trick to a place unsurpassed in its field. Paul Fox suggested the variation of using a red and blue backed pack, and then with the advent of roughing fluid Dai Vernon finally perfected the trick as we have It today.”

From Crimmins's history, it is clear that Vernon originally was performing the Brown effect and method, likely with some refined handling touches. Vernon corroborated this evolution of the Brainwave Deck in 1977, in an interview autotaped by Pat Page, marketed by Page in 1977 as an installment called “From the End of My Cigar” in his “Sounds of Magic” series. Karl Fulves, in A History of the Brainwave Principle (1983, p. 97), transcribed the taped conversation concerning the Brainwave Deck. There Vernon says:

“The Brainwave deck? I didn't invent it. […] I got some of this Slick Ace fluid and I made up a pack of cards. Then I thought, why force a card, why not get that effect with a Brainwave. It was like the Light & Heavy Chests, taking an old principle and presenting it in a different way. It was no invention because they'd often pushed two cards waxed together, but you'd have to break them apart. With this fluid on there you could handle them naturally.

“Paul Fox was the one—I first did it with an ordinary pack of cards. I used to do it face-up. The (thought of) card would be face-down. But Paul Fox said to me, why not put a different color card in there. Now, when you show it, the card is face-up like this, and you come to the card and you show it, the selected card, you say, 'You people may think I was clever enough to reverse that card in some way, but that's the only blue card in the deck.' That was a real effect.

“I did that before anybody. It was years ago. But it was no invention, it was just a switch on an old principle, that's all.”

In summery, while Vernon has been widely said to be the inventor of the “Brainwave Deck”, the role he played was more in the refinement of the method and in the popularization of the trick. Judson Brown gets the lion's share of credit, Paul Fox provided an important twist on the effect, and Vernon made a further improvement by changing the adhesive from wax to roughing fluid.

These are the essential known facts of the history of “Brainwave”. However, the story of its evolution is long and complex. In A History of the Brainwave Principle (1983), Karl Fulves offers an excellent and detailed look at how this effect evolved.