It's not possible to smoothly move your eyes unless you are tracking a moving object. Your eyes always move in saccades (quick jerky movements), unless there is a smoothly moving object, in which case your eyes gain the ability to track it smoothly.

https://www.shadertoy.com/view/tXSBWt

Here is a version with a smoothly moving red circle; notice how you can now move your eyes smoothly around the screen as you track the circle.