Gadadhara Pandita represents that bhava, and thus he is at the side of Mahaprabhu to assist him in his search. In this explanation, Gadadhara gives his bhava to Gauranga willingly. It has also been explained that Krsna has stolen the bhava of Radha and appears as Mahaprabhu, Radha Krsna combined. Gadadhara represents that which is left of Radha after Krsna steals her bhava. Gadadhara appears on the new moon and leaves the world on the same day.
New moon means no moon.
He also appeared in a land that is desert-like, dry and vacant in contrast to the lush Ganga basin of Navadwipa. All of this indicates the condition of Gadadhara. He is empty. What remains in him is the bhava of Rukmini, who is Radha's expansion in Dvaraka. He is submissive to the extreme.