Dawn -- good time to pick up I? On the contrary (3-2)

I believe the answer is:

get-go

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'dawn good time' is the definition.
The definition suggests a singular noun which matches the answer.

'pick up i? on the contrary' is the wordplay.
'pick up' becomes 'get' (I've seen this in another clue).
'i? on the contrary' becomes 'go' (I can't explain this - if you can you should give a lot more credence to this answer).
'get'+'go'='GET-GO'

'to' acts as a link.

Can you help me to learn more?

I've seen this clue in The Telegraph.

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