You ever play around with the buttons on your long glass?
Cookie has three cameras with two set up for back button. One is full frame, and second a crop. Both typically carry 100-400m zooms or get some smaller glass if conditions merit. Her big gun (EOS 70D) is equipped with a 500mm, and to date she's left it running with the default shutter/focus set up.
Agree totally on the eye, as that is where all the life is. That gets first glance when evaluating an image. If the eye's not sharp it goes the way of the delete button.
Extremely rare for us to do images of people, but if I'm behind the camera I insist that sun glasses come off for that same reason.
Edited for the addition below::
Cookie did this one a day or two ago, and I was amazed she even tripped the shutter. Canon 5D Mk IV with a 100-400 lens, F5.6, at 1/400 sec at about a dozen feet and the glass was able to essentially look through a ton of intervening brush to get at the bird (long eared). Focal point was on the bird's left eye, as I think there was a twig in front of its right.
Not something I'd enter in a competition, but at least she has a long eared owl shot now.