It's so odd that we use the ring finger to wipe our eyes. I just tried it (tested to see which finger was instinctive) and the ring finger is the one I used! I wonder why.
Perhaps because we subconsciously feel that the thumb, index and middle finger are dirtier than the ring and pinky (because they actually are - they come in contact much more with whatever we are handling, food or otherwise). Ans between the ring finger and pinky, the ring finger requires less contortion of the hand in order to wipe the eye than the pinky requires.