The story
From Zelig + -esque (suffix meaning ‘in the manner or style of’, forming adjectives from nouns (especially proper nouns)), referring to the character Leonard Zelig from the 1983 film Zelig who meets many famous people in the 1920s and 1930s and, apparently out of his desire to fit in and be liked, unwittingly takes on the characteristics of the strong personalities around him.
Etymology from Wiktionary, CC BY-SA 4.0.