Dance — pick second half or pick again (7)

I believe the answer is:

reelect

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'pick again' is the definition.
(I've seen this before)

'dance pick second half' is the wordplay.
'dance' becomes 'reel' (reel is a kind of dance).
'pick second half' becomes 'ect' (I can't justify this - if you can you should give a lot more credence to this answer).
'reel'+'ect'='REELECT'

'or' is the link.

Can you help me to learn more?

(Other definitions for reelect that I've seen before include "Bring to power again" , "put back in" , "Return to seat" , "Put in power again" , "Vote into office again" .)

I've seen this clue in The Hindu.

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