You are speaking of a locked-in person. At this point the expression of intelligence is still an action. In this case, moving the eyes.
This is still a very high level intelligence.
You really should be looking at a worm or similar creature for the most basic intelligence.
When you simplify the body enough the intelligence expressed is not very interesting.
Forum member @Gary_Gaulin has posted a bug creature that has a very basic intelligence. Check out the video in the linked post. That “bug” is driven by a very small chunk of “cortex like” intelligence.