In Section 13, the governess strikes a note of contradiction. She first admits that it's not yet definitely proved that the children are aware of the ghosts, and then a moment later, expresses the fear that Miles and Flora see more (that is, more of the ghosts and more of the hidden meaning) than she does.
The subject of the uncle's appearance is further developed in these sections. First, there are the letters the children write but which are never sent. Then comes Miles' demand that his uncle be consulted about his schooling. As much as the governess wants her employer to be pleased with her and to come to Bly, she is still frightened of the possibility that he actually will appear.
It is, therefore, while under the pressure of Miles' demand and the subconscious desire to see her employer that the governess once again sees the ghost of Miss Jessel. This time, the ghost appropriately appears in the schoolroom, which suggests there is a connection between Miles' demand for more schooling and the appearance of Miss Jessel in the schoolroom.
