I was wandering around the Gerudo Desert, and found a trail that ultimately lead to a nifty piece of gear. I warped back to Gerudo Town, and Riju had a quest. She said that there was this trail out in the Desert, which leads to a nifty treasure. Then Link explained that he'd already found the nifty treasure, and was in fact wearing it right now. Finally, I got the quest started popup, immediately followed by the quest complete popup.
Honestly, it's kinda nice how some quests are just pointers to things you could figure out on your own. It's kinda like the NPCs are acting like the mythical playground rumour mill.