Crossword Genius

Broadcast rock after reflecting greatly (3,4)

Ross

I believe the answer is:

big time

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'broadcast rock after reflecting greatly' is the definition.
I can't tell whether this defines the answer.

'broadcast rock after reflecting' is the wordplay.
'broadcast' becomes 'emit' (to emit is to broadcast or give out).
'rock' becomes 'gib' (both are nicknames for Gibraltar).
'after reflecting' is a reversal indicator.
'emit'+'gib'='emitgib'
'emitgib' written backwards gives 'BIG-TIME'.

Can you help me to learn more?

(Other definitions for big time that I've seen before include "Very important" , "To a great extent" .)

I've seen this clue in The Times.
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