Every one of Samkhya's five Jnanendriyas has a counterpart among the five gross elements, reached by way of one tanmatra, and chakshu's path runs through rupa to tejas, fire. The connection is not simply a shared name for "vision-related things"; it follows the same evolutionary logic that links every other organ-tanmatra-element chain in the system, each subtle element condensing into its corresponding gross element once enough tanmatras have accumulated to give it the necessary density.
The same correspondence holds from the elemental side: Tejas, fire, is traditionally described as governing digestion and vision and as carrying rupa, form and colour, as its associated tanmatra, drawn from the same Samkhya literature this entry draws on. Chakshu is the organ-side half of exactly that pairing, the sense faculty whose one object, form and colour, is also the specific quality fire contributes once the elemental sequence completes. Indian medical and cosmological writing outside Samkhya proper frequently repeats this pairing, associating visual acuity and ocular health with the body's fire element, tejas or agni, which is one of the clearer instances of a purely philosophical enumeration shaping practical, applied thought centuries after the enumeration itself was fixed.
Because the correspondence runs in a fixed order, subtle to gross, chakshu's position among the Jnanendriyas, third by most classical counts, tracks rupa's position as the third tanmatra exactly, and neither ordering is arbitrary relative to the other.