I'm interested in learning about the history of Dean's Box. My understanding is that the effect is influenced by:

"SEFALALJIA" by Stewart James(from Jinx)
"Loops Entwined" by Jack Avis (from The Phoenix)
“Linked” by Paul Curry (from "Worlds Beyond")

Specifically, I'm wondering about the second phase of Dean's Box routine, as performed here: https://youtu.be/dxLx6TqFQ0M?t=88

I'm not looking for the method, but the origin of that phase, where the box is opened and the rope pulled back and forth showing that it's connected. Did Dean create that phase, or is it from one of the above sources, or something different?

The first linking phase is "Loops Entwined".

I'm pretty sure the second phase was Dean Dill's own. It's certainly not in Sefalaljia or the Encyclopedia of Rope Magic which contains Linked (and Elizabeth Warlock's refinement, Link Later. It is, though, just a variation of Linked. At least I think so - you can see him doing the dirty work at 2'10.

Dean Dill learned the basic move from Harry Lorayne's The Magic Book. It is in the trick called Ultra Bind.

The exact handling of Phase II is a Dean Dill idea which was made possible by the little door on top of the box which could hold the loops. Dean would specifically cite that little cut out door, not the idea of a box, as his main contribution. Using a silk, envelope, or putting the loops under a table/behind the head as was traditionally done did not allow for the "cleanup" to happen prior to the link being shown. That is what the little door enabled.

Fair enough, but actually Link Later also contains a bit of hardware - a piece of wood with four slots in it - which accomplishes much the same thing.
I've never actually seen the linking of the ropes as remotely magical. The first time I saw it, it was obvious to me what was happening. The Sefalaljia move is much more deceptive (among boxes and rope tricks)