Ahh I think I now see were our ideas differ.
You indicate that closely guarding does not require obtaining LGP.
I think Situation 9.10.1.C addresses this nicely. Although used earlier in the thread I am going to quote it again:
Team A has the ball in its own FC. B1 stands within 6 feet facing A1 while A1 is holding the ball near the division line. RULING: In five seconds this would be a violation. In the sitaution outlined, as soon as B1
has assumed a guarding position, both feet on the court, facing the opponent, no other specific requirement is in effect. The amount of movement or the actual body position of the player is irrelevant" Emphasis added
As you probably recognize, the highlighted words reflect how LGP is initially established 4.23.2.
As you know situations supplement the rule book.
So in the example you outlined,
"Image B1 who takes a position between A1 (dribbler) and the basket (guarding).
However, B1 never faces A1 (no LGP). A1 is furiously attempting to drive to the basket but B1 constantly moves to cut off A1's path
while never facing A1. There is never any contact so LGP is not relevant. However, B1 continuously maintains a position that is 2'-4' from A1."
No count can start in this example until B1 "has assumed a guarding position, both feet on the court, facing the opponent" (Sit 9.10.1c).
So hence the only conclusion we can come too is that once LGP is established "PATH " (direction) has no bearing on guarding. and since "Closely guarding" requires LGP a violation (Closely guarded) should have been called after 5 seconds based upon the description in the OP. Seems like such a long time ago.
I hope this also answers BACK_IN_THE_SADDLE comments
Thank you both for your thoughts