For some reason, the unusual design of the Denny "Eye Knife" seems to baffle many carvers. In fact, I came to own one because a fellow carver could not get comfortable with it, so he gave it to me to figure out. I admit I haven't really tried it on eyes, so I too was unsure how this came to be called an eye knife. Even knives with names like "detail knife" don't specify what kind of detail. They're just small, pointed knives to be used wherever detail work is done. I found the eye knife useful on a tricky project where I needed a little extra blade tang to reach in and do some careful work. But it was not an eye. It was the inner cage of my cage in a cage carving.
Recently, I was doing a few Santa faces and I decided to see how the eye knife would best be used to carve eyes. I looked at the blade for a minute and wondered why the unusual dip on the back. Then I looked at the extremely angles skew blade.
Now I know a skew blade is not only well-suited for getting into tight corners, like the corner of an eye, but it excels at the slicing cut. If you want a smooth eye ball, a low angle, slicing cut is the best way to go. For this type of cut, I want to move the blade a small distance, with the greatest control possible. To me, that means bracing to tool against my opposing thumb and pivoting. I placed my left thumb (I'm carving righty) on the dip on the back of the blade and my right thumb on that and was able to carefully and accurately pivot the knife and slice across the eye. The right hand does all the moving. This knife comes razor sharp and leaves a beautiful, smooth cut across the eye.
A little practice with this and I found the knife to be perfect for the job it is named for.. I wouldn't suggest you need to go out and get this for eyes. Lots of knifes can be taught to do the job, but if you have the eye knife, languishing in your bag, why not take it out and give it another try.