Yes, it sets off from the tea garden on the back road in Fethiye.
If you were to walk up beside the big white mosque to where you'd normally catch an Oludeniz/Ovacik/ Haisaronu dolmus and then continue to the T-junction and turn right (against the flow of traffic), there's a tea garden about 200 metres down on the far side of the road. The Kaya dolmus runs between there, directly up over the hill and into the centre of Kaya.
Unfortunately I can't tell you the departure times, but they are displayed at both tea gardens and in the window of the dolmus.