Kirk describes Finnegan as a practical joker, who bullied Kirk with childish pranks. Yet, when Finnegan shows up, he antagonizes Kirk not with practical jokes, but Good Old Fisticuffs. Because this isn't Finnegan, but a wish-fullfilment construct version, who exists so that Kirk can have the joy of beating the tar out of him. Wouldn't be as much fun if Finnegan didn't put up a fight, and hit Kirk first, giving tacit permission to Kirk to beat him up.
The Caretaker mentions to Kirk that he believes that the Federation's people aren't ready for the reveal of their people, with Spock immediately agreeing. The Caretaker himself might just be A Form You Are Comfortable With or even one of the planet's constructs.
When Kirk leaves Spock to chase after Finnegan, he does a completely unnecessary leap over a rock in his path. It's a subtle clue that Kirk, likely on an unconscious level, has realized that his real goal isn't to solve the mystery of the planet, but to have fun whaling the tar out of an old nemesis.
