I just noticed the reproduction of Elliott's Sphinx article in Culliton's "Houdini the Key." Elliott attributes the pass to William Frazier, a card player. The description of the move seems to apply to the card table, where the deck would be held horizontally.
The gist of this pass is to lift off the top packet with the left fingers and place the packet perpendicular to the deck as the right hand covers the deck during a squaring motion. At the end of the squaring motion, the audience sees the bottom half of the deck and thinks it is the whole deck. With the top packet covered by the right hand, it can be brought under the bottom packet slowly or quickly. I assume that the spectators are looking down at your hands.
Interestingly, Elliott suggests the technique, which Ganson mentions in "Dai Vernon's Ultimate Secrets of Card Magic," of nearly kissing the passed packets face to face and then curling in the left fingers to position the new bottom packet face down.
The Frazier pass is similar to the move that Gaultier calls Harry Houdini's Pass with Two Hands. But Gaultier talks about the right hand being "brought over" the deck and doesn't specify that it touches the deck in a squaring motion.
It also seems to be similar to the Houdini Card Pass in Houdini's book about Elliott. It talks abut the right hand being free of the deck when the top packet is moved. So it sounds like Houdini claimed at least independent invention of that version.
So maybe that's what distinguishes Houdini's pass from Frazier's pass: lifting the top packet, perpendicular to the deck, into the right hand as it screens the deck from a slight distance. That sounds like it's better suited for the stage, where the performer can turn to his left and hold the deck vertically. I don't see how you'd get away with it close-up or at a table.
Confusingly, the move called the Elliott Pass in Houdini's book about Elliott is more similar to Houdini's pass than to Frazier's pass. The right hand isn't on the deck when the top packet is moved.
One difference from Houdini's pass is that the bottom packet is levered above the edge of the upper packet, which then can be placed under the former bottom packet by simply curling in the left fingers.
Reading more closely, I see now that Farelli didn't have the Sphinx article in front of him, so I'm guessing that he didn't remember Elliott's credit of Frazier. Farelli's description of the Elliott Pass includes the squaring motion, while the move he calls Variation of the Houdini Method has the top packet lifted into the right hand before that hand grips the deck.