Zach hadn't brought Nora along to the south because…
He had left her behind since she…
He thought she didn't want to tag along after…
Maybe she was busy?
Zach couldn't come up with an excuse. There hadn't been enough Labyrinth Tickets so Zach simply hadn't thought to make her go with them just to wait around while they entered the Labyrinth.
He knew she could take care of herself, but there was no reason to make her take care of herself in the middle of what could have been pirate territory when she could spend her break in the Academy, relaxing, training, studying, cleaning, cooking, playing, and fishing.
Zach almost thought he had been considerate in giving Nora a vacation.