Both Heel Vessels terminate at the eye, and classical Chinese medical theory ties the pair jointly to the mechanics of the eyelids and to eye movement generally, treating certain patterns of eyelid drooping, excessive blinking or difficulty closing the eyes as signs of an imbalance between the two vessels rather than as problems localized to the eye alone.
That eye connection, alongside the pair's role in leg movement and the sleep-wake cycle, illustrates a broader feature of the extraordinary vessels as a category: several of them link body regions, in this case ankle and eye, that have no obvious anatomical connection through the twelve regular channels, giving practitioners a way to explain symptom patterns that cross regions the regular channel maps do not directly join.
The meeting point is specific. Both vessels are described as terminating at Bladder 1, at the inner corner of the eye, which is where their courses converge after running the length of the body on opposite aspects of the leg. A pair defined by opposition along its whole route ends at a single shared point, and the eye is where the alternation between them becomes visible from outside: whether the lids are open or closed is the plainest indicator the system has of which vessel currently holds sway.
That is also why the classical sleep account and the classical eye account are not two separate claims about these vessels. Closing the eyes and entering sleep are one transition described at two scales, and the texts treat them together.