Kaytoo looks up to Deathtrap, the red optics a familiar sight. Back to Gaige:

"I've decided I want you to win. Please allow me to see your paint-blaster."

He doesn't know why he's decided to help her cause- she doesn't remind him of anyone he knows really. Maybe it's her interest in him, maybe it's another glitch, or maybe it's because she said he was 'awesome.' He likes being awesome.

Mostly, he thinks it's a good way to kill time.

"I will return it to you."