Hi Lilac: theres at least one person who does Reiki and hasnt got an open Third Eye - me!
There are almost as many opinions on what the Third Eye is, its function,its purpose and how it gets opened as there are people expressing them: this is not to undermine the idea, it is clearly established in both Buddhist and Hindu tradition as well as older aboriginal traditions, however the third eye and its uses are not mentioned in the earliest Reiki writings and were probably added on when Chakras were added to the system of some lineages.
I know someone who (expensively!)trained to Masters level with the Furomoto tradition and had her third eye "opened" along with instruction on how to see auras for diagnostic purposes, and the whole sheebang was no more specific to Reiki or "spiritual" than the recent useful posting on the subject on this site. For me, I prefer to develop my "Reiki Intuition" that has always stood me in good stead, besides, if my third eye opened I'd have to shave my eyebrows as they tend to meet in the middle!
Good luck with your researches, you are sure to get some interesting replies.
Skyhorse.
