Green’s Dictionary of Slang

(US) an important or self-important person.

1908		L.W. Payne Jr ‘Word-List From East Alabama’ in DN III:iv 320: high-muck (-a-muck), n. Chief officer, boss, manager, leader.
1953		Sat. Eve. Post 18 Apr. 57: Will the high mucks not give you a helpful hint, Doris? [HDAS].