Desert island left having good grounds (8)

I believe the answer is:

rational

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'having good grounds' is the definition.
I can't judge whether this definition defines the answer.

'desert island left' is the wordplay.
'desert' becomes 'rat' (abandon treacherously).
'island' becomes 'iona' (Scottish island).
'left' becomes 'L' (common abbreviation).
'rat'+'iona'+'l'='RATIONAL'

Can you help me to learn more?

(Other definitions for rational that I've seen before include "Logical; sensible" , "Endowed with reason" , "Reasoning, logical" , "Based on logic or reasoning" , "Not absurd" .)

I've seen this clue in The Times.

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