This symbolism in particular is all over Hollywood. Most of the time, they show the left half of your head (or the left eye) in the shadow, fiery, burnt, etc whereas the right side is shown as the normal, clear side. So what does it represent?
Here is a collection of 'occult' symbolism including the one I have mentioned.
I believe that this symbol is wrongly attributed only to freemasonry, since it is a very ancient symbol (Egyptian Pantheon), representing the Eye of Horus, the panopticism of God (the right side eye). As far as it concerns the left eye, the Eye of Thoth, the Scribt of Gods of the Egyptian Pantheon, represents "karma" (punishment or reward).
As I understand it the right eye is the eye of sending, and the left eye is the eye of receiving. Perhaps by covering the left eye it symbolizes that they are sending a message. Just a thought I'm having at the moment.
Also the right side of the body is sometimes attributed to good, and the left side attributed to bad or evil. This may play an important role in our understanding of left and right in a spiritual sense. If thought of mathematically the right side of a spectrum of numbers is the positive, so the left side is the negative, and zero is null and void of negative or positive. The same principle can be applied to the body.
Maybe the right side is truth and the left is left?