Searching good girl for a mirror (12)

I believe the answer is:

lookingglass

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'a mirror' is the definition.
I know nothing about this answer so I can't judge whether it can be defined by this definition.

'searching good girl' is the wordplay.
'searching' becomes 'looking' ('look' can be a synonym of 'search').
'good' becomes 'g' (abbreviation).
'girl' becomes 'lass' (lass can informally mean a girl).
'looking'+'g'+'lass'='LOOKINGGLASS'

'for' is the link.

Can you help me to learn more?

(Another definition for lookingglass that I've seen is " image seen here?".)

I've seen this clue in The Daily Express.

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