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Close look at objective of insomniac (4-3)

Ross

I believe the answer is:

shut-eye

'objective of insomniac' is the definition.
(an insomniac wants sleep or 'shut-eye')

'close look' is the wordplay.
'close' becomes 'shut' (synonyms).
'look' becomes 'eye' (eyeing is a kind of looking).
'shut'+'eye'='SHUT-EYE'

'at' acts as a link.

(Another definition for shut-eye that I've seen is " Sleep".)

I've seen this clue in The Telegraph.
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