the terangreal is broke maybe or its inactive for avi, or for everyone, maybe whatever lives inside it, construct or otherwise, was freed by avi or by someone else before she got their, and was getting ready to leave for fun and adventure? its just a possibility it was a housing for a construct, a true dragon perhaps lived inside it? again just at hought, that said aviendha is also powerful and important, she presents the average wise one and explains how they are, the most we see are dreaming wise ones, which are different, so her behavior shows how nondreamer wise ones are too.
I would guess the aiel are destined to become red shields as a clan, to act as a honor guard in cities similar to red ajah