Little example of how you can make eye rig
Addons used:
timecodes:
00:00 Intro
00:14 Part 1: Deformation and Tweak bones
11:08 Part 2: Eye controls and mechanism bones
16:05 Part 3: Eyelids controls and widgets
23:25 Part 4: Corrective shapekeys
27:20 Part 5: Eye bulge with Warp modifier
29:55 Part 6: Animated normals
33:22 End result