'autonomical' originates from Greek 'autonomos' (through New Latin/Modern Latin and English formation), where 'auto-' meant 'self' and 'nomos' meant 'law' or 'rule'.

'autonomical' developed in English as an adjectival formation from 'autonomy' / 'autonomos' (Greek). The Greek 'autonomos' ('auto-' + 'nomos') passed into scholarly Latin/Modern Latin and then into English as 'autonomy' and related adjectives such as 'autonomic' and 'autonomical'.

Initially it meant 'self-governing' or 'having its own laws'; over time it has retained that core sense but has also been used (rarely) to describe functions of the autonomic nervous system.