The solution is easier than it looks
“Waiting All Day and Night” is an extraordinarily early quest in Octopath Traveler 2. It’s located just outside the tavern in Canalbrine, where you’ll find a Waiting Youth sitting at the outdoor table waiting for someone. To finish the quest, you’ll have to unite these two people that have seemingly lost each other.
This is one of those quests that looks obtuse at first, but the answer is right in front of your nose. To complete it, you’ll need at least one party member who can recruit NPCs to the party. This could be either Temenos or Agnea during the daytime, with Partitio or Ochette also doing the job at night. If you don’t have any of those characters in your party yet, recruit at least one of them and come back to this spot. Here’s how you solve this quest.
How to find the person the Waiting Youth is searching for
You’ll notice the Waiting Youth’s seat is occupied at both morning and night, but the situation isn’t what it seems. Use a Path Action to recruit the Youth, and then immediately switch the time of day. Surprise, you’ll still see someone sitting in that seat once the transition finishes! Talk to the “new” NPC and a short scene will play out.
Turns out, it was a set of twins who were waiting for each other at opposite times of the day. You will receive a Magic Nut, Empowering Lychee, and 3000 Leaves for your troubles before the quest formally concludes. With that out of the way, feel free to continue your quest!