Mobile cover, essential to winking and blinking! (6)

I believe the answer is:

eyelid

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'essential to winking and blinking' is the definition.
I can't tell whether this defines the answer.

'mobile cover' is the wordplay.
'mobile' becomes 'eye' (I am not sure about this - if you are sure you should believe this answer much more).
'cover' becomes 'lid' (lid is a kind of cover).
'eye'+'lid'='EYELID'

Can you help me to learn more?

(Other definitions for eyelid that I've seen before include "Protection for organ of sight" , "Natural optic occluder" , "Blinking cover" , "Facial feature" , "One winks with it" .)

I've seen this clue in The Irish Times.

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