eyes remaining open (due to insomnia)

stare into space (while contemplating)

look on helplessly

(adverb) to describe when someone is looking vacantly / gazing aimlessly / staring blankly into space, as though they are comtemplating something or distracted in their own thoughts; to describe how someone is looking on helplessly; to describe how someone is gaping / gawking eagerly; to describe how someone is gazing longingly; to describe how someone is looking on expectantly; (adj.) eyes wide open, to describe someone who is wide awake and cannot sleep at night