That experience became his political awakening.
目覚め highlights the literal or figurative moment of becoming awake or aware, whereas 寝起き is a plainer word for the everyday act or state of waking up.
Standard kanji spelling; commonly used in news and everyday writing.
Search-only mixed kanji-kana form; not a standard spelling.
Rarely used kanji form; 醒 carries a nuance of sobering up or awakening from a dream.
Compound of 目 (eye) and 覚め (noun form of 覚める, to wake). The kanji 醒 in the rare form 目醒め adds a nuance of sobering or clarity.