Graduate starts living in open enclave south-east of popular island of Indonesia (8)

I believe the answer is:

balinese

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'popular island of indonesia' is the definition.
I can't tell whether this definition defines the answer.

'graduate starts living in open enclave south-east' is the wordplay.
'graduate' becomes 'BA' (someone with a Bachelor of Arts degree).
'starts' indicates taking the first letters.
'open' says to take the initial letters (take the opening letter).
'south east' becomes 'SE' (abbreviation).
The initial letter of 'living' is 'l'.
The first letter of 'enclave' is 'e'.
'ba'+'l'+'in'+'e'+'se'='BALINESE'

'of' acts as a link.

Can you help me to learn more?

(Other definitions for balinese that I've seen before include "policy needs external support" , "Asian language" , "Indonesian" , "Foreign language" , "Islanders" .)

I've seen this clue in the Sydney Morning Herald.

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