What is the rest state for eyelids - Open or Closed?
This depends to some extent on how you define "resting state" (it matters). 

Innervation of the eye occurs in the brainstem and upper spinal column, so is, like most brainstem functions, on autopilot (like breathing.)

If you define resting state as that which the lids would assume without any innervation, then the resting state of the eyelids is semi-open. This is the state of the eyelids of most people who die. 

However, that position is not beneficial to the living eye, as it would lead to corneal breakdown. When people lose eyelid innervation, for example, following a stroke, the lids don't close completely. Ointment must be applied several times daily and the eye is often taped in the shut position to protect the cornea.

If you define resting state as that which occurs in sleep and in most comatose states, the eyes close completely, because innervation of eye muscles is intact and a main function is to protect the cornea, i.e. vision. This is done with a completely closed eye.

Comprehensive Review in Clinical Neurology, Cheng-Ching et al.