FWIW the eyeball on that image looks less sharp than the eyelashes are to me. Actual image is here
Possible "solutions:
If you are prepared to post-AF manual focus you could use AF and then back focus very slightly
or focus on the inner corner of the subjects left eye.
or (cheating :-) ) move in by the physical amount needed,
or (very cheating) micro-adjust your AF by the desired amount.
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Do cameras that have an Eye AF features such as the Sony A7r II consistently focus on the iris?
I know not but most Sony's (and the A7RII will be included) have "focus peaking" which allows you to either
Use AF then check the result with the Af/MF toggle button or
Manual focus with utter [tm] precision or
Use AF as above then toggle manual/AF toggle (button press by right thumb when focusing) which turns on focus peaking mode and tweak focus if/as desired manually.
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Added: The following is re focus peaking on Sony cameras "which you have not got" (although they did make your sensor). I'm adding it as it is relevant to the general situation that you describe and may be useful to others, even though not necessarily applicable to your current hardware. [I do not know if Nikon implement focus peaking but as the D750 uses a Sony sensor they presumably could].
"Focus peaking" in Sony's implementation adds a colour overlay to areas which are in-focus. [One of white/red/yellow highlighting canm be selected and the degree of highlighting can be varied. I find this feature immensely valuable in selected cases where very precise focusing is required. This may be eg
In the presence of multiple alternative closely grouped focus targets - such as a bird in the middle of leaves part way through a tree
Where a single very small target is spatially isolated such that it is unlikely to be a preferred auto-focus target - such as a single grass stem physically separated from other objects.
On a surface at an angle to the line of view such that there is a physically continuous line on which focus may occur but a specific point is desired.
A combination of two or more of the above such as links on a fine chain suspended on space such that AF tends to miss the chain and a specific link is the desired focus point.
Focus peaking's main issue (for me) is that it appears to be contrast based and in some targets highlighting is less positive depending on image content. It can almost always be used once the user is familiar with it.