As I remember Sakura search in river view in afternoon,and for Amaya if I remember you need to walk in night and it's randomly the event appear.
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sakura event is not random,I think when you see on the quest when you already got enough passion? I think or relationship with Sakura you will get the mission to find sakura.
And I think this mission is after the celebration party mission when she realizes Sasuke not really love her and just do misión and mission(in this game though)
So it's not random.
Amaya one will random at night,just walk.