Using an Orientation Constraint to make one eye follow the other.
 

Step 1
Go to the Motion panel, expand the Assign Controller menu, select Rotation, and click on the Assign Controller button (the question mark).

Step 2
Select Orientation Constraint from the list.

Step 3
Scroll down the panel and select the Add Orientation Target button.

Step 4
Select the other eye as the target.

Step 5
At this point you're all set and can safely ignore the original eye and just animate the eye you selected as the target.

While this is pretty easy to set up, it's not a very efficient way to animate.

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