Eager to join TV phone-in broadcast via the bush telegraph (2,3,9)

I believe the answer is:

on the grapevine

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'via the bush telegraph' is the definition.
I know nothing about this answer so I cannot tell whether this works.

'eager to join tv phone-in broadcast' is the wordplay.
'to join' means one lot of letters go next to another.
'broadcast' indicates anagramming the letters.
'tv'+'phone'+'in'='tvphonein'
'eager' after 'tvphonein' is 'tvphoneineager'.
'tvphoneineager' is an anagram of 'ON THE GRAPEVINE'.

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I've seen this clue in The Guardian.

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