Although they certainly popularized it and "took it to the next level," we all know by now that guitarists Stanley Jordan and Eddie Van Halen did not invent two-handed tapping.
Some sources claim it started centuries ago (albeit on other instruments), and people like Roy Smeck, Harry DeArmond, Jimmie Webster, George Van Eps, Barney Kessel, Emmett Chapman, Harvey Mandel, Randy Resnick and Steve Hackett had been spotted doing it long before the rise of Jordan and Van Halen.
A YouTube video shows another guitarist, an Italian radiologist named Vittorio Camardese, showing off his own two-handed tapping technique on an Italian TV show (on the RAI network) in 1965.
In the video, Camardese says he's an amateur guitarist who works at Rome's San Filippo Hospital. He says the guitar was lent to him by a friend at work.
If you don't want to listen to their conversation (which is in Italian), skip ahead to 1:14, although the real playing starts at 1:30. After a break and some more chatting, Camardese starts playing "All of Me" at 3:10. He breaks into some tapping again at 3:53, complete with what looks like devil horns (\m/).
Anyway, a big shout out to Mr. Camardese, wherever he might be! Enjoy!
P.S.: Because we didn't feel the need to mention everyone, we've excluded some names from our "pre-EVH two-handed tapping pioneers" list above. Feel free to add names in the comments below! One commenter has already pointed out Dave Bunker (Watch a VIDEO here).