Some smooth muscles that we can’t control voluntarily are controlled by both the parasympathetic and sympathetic nervous system.  Others only have one or the other.  The droopy upper eyelid or ptosis is caused because we stop the functioning of one of such smooth muscle in your upper lid.  The pupil size becomes small under predominantly parasympathetic control when we take away the sympathetic nervous system influence.  Similarly, the nostril on the side of the blood becomes engorged and swells without the sympathetic nervous system influence.