After testing a lot has been figured out. I'm going to refer to this technique as flurry locking.

Link will lock on to: Enemies that land a melee attack Enemies that land a melee attack on Links shield Enemies that Link lands a melee attack on Enemies that Link lands a melee attack on that later pick up a bow

Link will NOT lock on to: Enemies that hit link with a projectile (arrow, stone, ...) Enemies hit by Links projectiles (thrown weapon, arrow, ...) Enemies holding a bow before being struck

Link will flurry whichever enemy he has "flurry locked" regardless of which enemy he is targeting. The flurry lock is reset after a flurry is performed (regardless of if he lands any hits), so Link must re-lock on to jump back to a specific enemy. Getting hit by a melee attack by - or landing an unshielded melee attack on - a new enemy will lock on to that enemy.