Left beside desert island, able to think clearly (8)

I believe the answer is:

rational

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'able to think clearly' is the definition.
I can't judge whether this defines the answer.

'left beside desert island' is the wordplay.
'left' becomes 'l' (common abbreviation).
'beside' says to put letters next to each other (I've seen this in other clues).
'desert' becomes 'rat' (abandon treacherously).
'island' becomes 'iona' (Scottish island).
'rat'+'iona'='rationa'
'l' after 'rationa' is 'RATIONAL'.

Can you help me to learn more?

(Other definitions for rational that I've seen before include "17 [INTELLIGENT]" , "Endowed with reason" , "Of sound mind -- not a liar (anag)" , "Thinking - not a liar (anag)" , "Agreeable to reason" .)

I've seen this clue in The Independent.

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