Crossword Genius

Brain division church dissenter left with little hesitation (10)

Ross

I believe the answer is:

cerebellum

I'm a little stuck... Click here to teach me more about this clue!

'brain division' is the definition.
The answer and definition can be both body parts as well as being singular nouns.
Maybe they are linked in a way I don't understand?

'church dissenter left with little hesitation' is the wordplay.
'church' becomes 'CE' (abbreviation for Church of England).
'dissenter' becomes 'rebel' (rebel is a kind of dissenter).
'left' becomes 'l' (common abbreviation).
'with' is a charade indicator (letters next to each other).
'little hesitation' becomes 'um'.
'ce'+'rebel'+'l'+'um'='CEREBELLUM'

Can you help me to learn more?

(Other definitions for cerebellum that I've seen before include "motor controller" , "bit of brain" , "part of the brain" .)

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