Fred Johnson wrote

Could static electricity to the eyeball cause lasting harm?

Unlikely. Don't think it ever produces a sore or anything
with the normal sort of static that you are likely to get.

Normally you just jump and swear with a static shock to
your finger etc, but I've found two instances on google
of pain lasting a few days when someone got a shock
on their nose (one in a shop from a perfume bottle
they were smelling, and one from a blanket at home).

But what if it got your eyeball?

Should be fine.