Picked up Asian needing sunshine in Asian island (6)

I believe the answer is:

taiwan

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'asian island' is the definition.
(Taiwan is an island in Asia)

'picked up asian needing sunshine' is the wordplay.
'picked up' shows a homophone (sound like).
'asian' becomes 'Thai' (from Thailand).
'needing sunshine' becomes 'wan' (I can't explain this - if you can you should believe this answer much more).
'thai' sounds like 'tai'.
'tai'+'wan'='TAIWAN'

'in' acts as a link.

Can you help me to learn more?

(Other definitions for taiwan that I've seen before include "Non-mainland China" , "China Sea island, strait" , "Island in East" , "Disputed island off china, used to be Formosa" , "Chinese island" .)

I've seen this clue in The Times.

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