Crossword Genius

Following the party line, singles wise to drink last of rum (2,7)

Ross

I believe the answer is:

on message

I'm a little stuck... Click here to teach me more about this clue!

'following' is the definition.
Both the answer and definition are singular nouns.
Perhaps there's a link between them I don't understand?

'the party line singles wise to drink last of rum' is the wordplay.
I cannot really understand how this works, but
'wise' could be 'sage' (similar in meaning) and 'sage' is found in the answer.
'of' could be 'o' and 'o' is present in the answer.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for on message that I've seen before include "Following official line" , "keeping to the script" , "in accordance with policy" , "Reflecting the official line" , "Following party line" .)

I've seen this clue in The Guardian.
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