Pleakly was a neurotic wimp with a lack of understanding of Earth.
In the tv show and later films as he was more accustomed to Earth we saw less of his neuroticism and he became more outwardly flamboyant. The drag thing which started out as "haha he doesn't understand Earth culture" became more "haha he really likes wearing dresses".
Him and Jumba also started to bond quickly with what started out as two differing comic reliefs that hate and are forced to put up with each other evolves into a strong friendship with multiple jokes revolved around them acting like a old married couple even when they aren't in their disguises. So you can argue they're relationship is somewhat similar to Red and Purple's.