Use the ring finger for the eye area !
The ring finger is is more sensitive than other fingers, so this is the finger you should use whenever you are doing something that needs a gentle and light touch. The skin around the eyes is very delicate since it is thin and does not have any oil glands. So, when massaging around your eyes, applying an under eye cream, or blending in concealer -- use the ring finger.
The nerves on the index and middle finger are numbed due to being used all the time for everything; these fingers are strong but not very sensitive. Use them when you need a firm, strong touch, such as for massaging the rest of the face.
The little finger is sensitive too, but usually we have less control over it's movements. Makeup artists use it when they need a "small applicator", for example when applying a highlight to the inner corner of the eyes.
Photo by Eternal*Voyageur