When you look at training and coaching as being instead of correcting or perfecting skills and their signifiers, but as "how you learn to learn," in that domain, a quiet eye is not an objective, but rather an effect of building skills on top of a set of underlying attitudes.

Goodhart's Law has been quoted a lot here recently, (re: measure becoming target and ceasing to be good measure), but it applies here.

The more useful question is, "of what is a quiet eye the effect?"

At an elite competition level, the physical differences (and scores) between athletes are so minor that success is more an effect of psychological habits than the relative difference in diet and training regimens.

Watching very top athletes, they are usually calm and deliberate, which is the effect of being in a zone where they are not intellectualizing or reacting to events, but are instead, in a state I call accept-respond. There is a huge aspect of ego suppression they can cultivate, where the y aren't distracted by hypotheticals, counterfactuals, and in particular, expectations and anticipations for how the immediate situation plays out, which delays their ability to shorten their accept-respond loop.

The very existence of an "if this then that," thought in their mind is performance inhibiting, because even that "if," statement needs to be negated before they can respond. Bringing conditionals to the game only works when the game plays out according to that conditional at the right time. At a learning level, you can learn those conditionals as tactics, but you need to practice them to where there is no conscious selection and evaluation of them when you are performing.

IMHO, a quiet eye is the effect of how you related to your trainer/coach/parent/teacher, and it's not incumbent on the student or athlete to develop it, it is the sign of a good teacher.