One profession, five schools
Gion Kobu dances kyomai of the Inoue school; Miyagawacho, Pontocho, Kamishichiken and Gion Higashi use the Wakayagi, Onoe, Hanayagi and Fujima schools of nihon buyo. I hold the shihan rank of the Fujima school, awarded within the school's own system, and I have no connection with Gion Higashi's teachers. When I watch any kagai I am watching a related tradition with its own lineage and repertoire, and I will try not to judge it by my rules.
The knees
The first thing a teacher looks for is whether the knees stay soft and the hips low, so that the head travels in a straight line and the sleeves do not bounce. In a maiko this is still being built, and I expect the visible effort to be part of what audiences find beautiful. I have not yet sat in a Kyoto theatre with this question in mind; that is what the visit is for.
The fan
A fan can be a cup, a letter, rain, a moon. The test is whether it opens without the wrist showing the work. The Agency for Cultural Affairs describes kyomai's Noh and puppet-theatre roots and its restrained, weighted movement, and Inoue-school dancers speak of mai rather than odori; I expect the fan to stay closer to the body than in the pieces I teach, and I will check that expectation against what I see.
The eyes and the pause
The gaze arrives before the body. The pause, ma, is where an audience decides whether the dancer means it. These are the two things I most want to teach a visitor in a single lesson, and the two things a maiko spends years on.
What I will do in Kyoto
Sit at one of the October recitals or at Gion Corner with a notebook and write down, for one piece, what the fan did and where the eyes went. Then rewrite this note with what I actually saw, keeping this version as the record of what I expected.