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 tell whether this definition defines the answer.

'left beside desert island' is the wordplay.
'left' becomes 'l' (common abbreviation).
'beside' is a charade indicator (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' put 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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