How to Make an Eye Target Bone Move Eye Bones? (Flat Eyes) First let me start by saying something that might help get rid of any confusion.  I made all the bones look like curves.  I will be calling these "bones" rather than calling them curves for this post to also help get rid of any confusion.  Please refer to the photo to help you understand what I'm doing.

So, I need the character's eyes to look at the target bone.  There are some things that I do not want to change so please don't share a method that will require me to change one of the following: 

1.) The pupils are flat cylinders that I want to move around on the lens.  I want them to be cylinders, I know there are other ways of creating pupils on a character but this is what I think is best for this character set=up.

2.) I want the eye bones to be close to his eyes so I can move them easily when I don't need the target in certain situations.  Actually, controlling the eyes with individual eye controls and being able to switch between that and an eye target is a common thing in rigs.  Anyways, I want to keep the eye bones.

3.) I want the target bone to move the eye bones, but parenting is not how it should be done because if you want the character to look far left or right and move the target to where it the character would be looking, the pupils will actually go out of his lenses.  So there needs to be some kind of thing, if the target is far away from the eyes and the target moves a lot, it will only move the eyes a little, but if the target is close to the face, it will move the eyes almost as much as the target gets moved.

You see what I'm trying to do?  I just want the character to look at the target when I'm animating with the target, but the target moves the eye bones.  When those eye bones move, that moves the pupils on the eyes.  That way I can choose to animate the eye bones themselves, and/or the target, to move the eyes.  

Does anyone know how to do this?  Thanks.
I assume that your "curves" are custom shapes for your bone rig. You can add a simple "damped track" bone constraint to the pupil's bone, pointing to the target; then you can animate the "influence" parameter to control the pupil either with the target bone (influence 1.0) or the pupil bone (influence 0.0).