Stan Wright wrote::)
I seem to remember reading something about setting the hook by pushing DOWN on the rod.
If you drop the rod with a quick snap, then lift the rod... the tip of the rod springs up and sets the hook.
More research needed me thinks.

Stan, I found a web page with the title at the top listed as " this is the secret of lantern fishing"
これがちょうちん釣りの極意だ! ( Kore ga chō-chin-dzuri no gokuida! )
http://ojin.nobody.jp/tenkara1.htmGoogle translation is pretty poor but from what I could decipher it pretty much matched your description - shake the pole initially with a push downward, which lifts the rod tip. Followed by lifting the rod.
Also mentioned is that the technique requires the line be in 'tension'. ie tight lines. Probably easier when using the lantern fishing set up which has a long pole and short line of only about 1.5 to 2.5 meters. There also seemed to be mention of this movement being a technique borrowed from Kendo and another term that when I googled it I found some images of resonance of a pendulum. So maybe some reference to the resonance of the length of the pole. I think.
Anyway, there could be some situations where the technique of initially snapping the pole downward, followed by lifting the rod will increase the success of a hook set.
After reading your post I did get out one of my tenkara poles and I could see the the tip does rise when the pole is first pushed downward. Probably works better the longer the rod. The rods for lantern fishing, with bait, appear to generally be as long as the longer tenkara rods or longer. I haven't tried it while fishing yet.
A typical lantern fishing setup from another web page " Introduction to Lantern Fishing"
ちょうちん釣り入門 ( Chō-chin-dzuri nyūmon )
http://teamoutdoor.nobody.jp/chochin2.html渓流ちょうちん仕掛け ( Keiryū chō-chin shikake ) Stream Lantern Work ; work = trick or setup.

fwiw