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to be mentally slow; to be befuddled
to become engrossed in; to become absorbed in
to become frayed and dishevelled (of hair, grass, etc.); to be fluffy
「惚ける」 has other readings with different meanings.
祖父はすっかり惚けてしまった。
My grandfather has completely lost his faculties.
祖父は最近少し惚けてきたようです。
My grandfather has become a little senile lately.
惚けた振りをしながら実は聞いていた。
He was actually listening all along while pretending to be oblivious.