Searcher wielding rod more beatific after drink (5,7)

I believe the answer is:

water diviner

'searcher wielding rod' is the definition.
(someone looking for water with a divining rod)

'more beatific after drink' is the wordplay.
'more beatific' becomes 'diviner'.
'after' means one lot of letters go next to another.
'drink' becomes 'water' (I've seen this in other clues).
'diviner' after 'water' is 'WATER-DIVINER'.

(Another definition for water diviner that I've seen is " Dowser, traditionally using a forked stick".)

I've seen this clue in The Times.

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