I walked to Kayaköy, a village some 5 or 6 miles from Fethiye. This is one of some pictures I took. Much of the walk was uphill, so some good views and gradually just trees and more trees. I walked along the road that cars may use, and it being Sunday it was busy. Also there were many off-the-road motorbikes, loud and indeed sometimes taking the small tracks I also used to cut off corners.
I was later informed there is an old, now mainly pedestrian, road that seems to be easier and lower (I had to climb to 357 meters, then go down.
My guess is this is a cistern.