‘Turtling’ is ‘turtling’ IMO no matter what you're looking at.. Doesn't have to mean turning away either IMO.. When one person is overwhelmed by their opponent they often turtle, even in high level competition, you will see folks just cover up or any number of things that fall into this category, sometimes it’s even a tactic as when Muhammad Ali did this kind of thing in Ropeadope....
Not sure what the idea is of staring the opponent in the eyes..
As far as what to look at... We teach folks to think and see of the opponent as a ball of energy, to face this "ball" and to visualize the entirety of this mass, and attack it's center..
Another thing we have always said is not to get scared backward, rather, get scared forward... If this works in terms of tactics, as it does for us, then I think it can help.. Face, follow, attack and get scared forward.. Meaning when you get scared don't go passive; go offensive with it.
Oh, and I like Marcus' 'smile thing'...
Probably posted this long ago… I picked this up years ago from one of my teachers.. Always smiling, esp when challengers would visit the school.. Very disarming.. and is supposed to automatically release certain chemicals into the brain that aids in helping us relax and stay loose.. I have also used this on freaks trying to stare me down.. It works very well. Not sure how a big ol' smile would translate over for women used against someone staring at them, has to be just right...

But a confident smile, and awareness as I mentioned in another post is a powerful street threat deterrent..
I think from a distance breif polite eye contact is correct.. No goading..through emotional transmission IMO..
If they move in, then 'awareness eye contact' I think is correct.. It says, I see you coming and I am ready..