What the secret agent did when it started raining? (4,10)

I believe the answer is:

went undercover

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'agent did when it started raining?' is the definition.
I don't know anything about this answer so I cannot judge whether it can be defined by this definition.

'what the secret' is the wordplay.
'what' becomes 'went' (I can't justify this - if you can you should believe this answer much more).
'the secret' becomes 'undercover' (I've seen this in another clue).
'went'+'undercover'='WENT UNDERCOVER'

Can you help me to learn more?

I've seen this clue in the Sydney Morning Herald.

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