I'll start with one of the greatest portrait painters of all time: Anthony Van Dyck. The eye of this old man looks complete, but note that the pupil doesn't have a hard edge, there are no individual eyelashes. The eyebrows aren't drawn as a bunch of separate hairs either.
The only part that's really crisp are the highlights, and they're more prominent in the lower lid and the lacrimal caruncula (the little watery pit on the inside corner of the eye).
In this woman's eye by Andrew Loomis, the pupil is sharper, but the iris is softened on the left side, and the eyelashes and eyebrows are softened and unified. He chooses to downplay the caruncula and the fold over the eye.
In this detail of a portrait by John Singer Sargent (click to enlarge) both eyes are greatly softened. There are some crisp edges, but look where he places them. They mainly occur in the structural forms surrounding the eye, not details within the eye itself, such as the iris, pupil or little hairs.
Sargent spent as much time preparing the structure around the eye as he did painting the eye itself. He compared the process of painting an eye in its socket to dropping a poached egg on a plate. The subtle movement of muscles around the eye is what conveys the character of expression, perhaps even more the particular details within the eye.
Caruncula on Wikipedia