What's the Name of That Book??? discussion

Fictional, possibly fantasy, book about a girl and her older sister. The elder girl has Lapis Lazuli embedded in her teeth and many other people in the village do the same with other stones depending on status. The older girl is thought to be some manner of seer, with the ability to send out their spirit and use their senses outside of their body. The reason they believe this is because, despite the fact that she acts like a vegetable, is because her younger sister "speaks for her." A test is implemented and the younger sibling fakes as many tests as possible (even using a fly to fake the smell test that was made to find the one with honey).

I'm almost absolutely positive that the book you're looking for is The Lost Conspiracy/Gullstruck Island by Frances Hardinge. It lines up exactly with your description; the older sister is a "Lost," a gifted child able to separate her senses from her body. Except, now the heroine (Hathin) thinks her sister (Arilou) is just an idiot. Then there's a conspiracy that kills off all the Lost except Arilou, making her the scapegoat.
Hope that helps. It's one of my favorite books! And I agree; Arilou is a total vegetable.

I knew that was correct as soon as you said "Arlou" the name seems to have stuck in my mind. Thanks so much for finding it for me, I'm terrible with titles but I really wanted to reread it since I've forgotten the ending. Thanks so much!