This might come from historical ideas of how the eyes work. I know that in ancient India vision was explained as a light coming out of the eyes, and being reflected back off objects. I wouldn't be at all surprised if the same ideas turned up in Western history - it is a fairly natural explanation to come up with.

So, perhaps the metaphor is a historical misunderstanding of how eyes work, which has stuck as a fictional cliche.

Indeed, when I was very small I remember noticing for myself that vision had something to do with straight lines, and that therefore I could predict whether I'd be able to see something by working out whether there was an unobstructed straight line between my eye and it. At the time I too thought of it in terms of drawing lines from the eye rather than to it, so I'd tend to agree that it's a natural thing to think!

On the other hand, I'm not sure it ever occurred to me to think of the thing coming out of my eyes as light. Light was obviously stuff that came out of bulbs, the sun, and other such things. I thought of what came out of my eyes as sight. Hmmmm.