This is what I call the 3rd period:
The 1st glyph is identical with those in the 1st and 2nd periods, as far as I can see. But the 2nd glyph differs by having what looks like a wing in front of the right arm. This is not, I believe, a 'misprint' but an intentional sign. What is its meaning? As wings are used for flying it perhaps means that the Moon now is flying up in the sky instead of being at the horizon. The Moon has lifted.
And the 4th glyph from the left might show the same thing, its round eye bringing to mind the Moon now beginning to look round (instead of earlier looking like a canoe sailing in the western sky). The theme of roundness is affirmed by the 7th glyph indicating hua and by the 9th glyph which looks as pregnant as the 2nd glyph.
But the eye might also mean alertness. From its sleep in the darkness of the New Moon phase the Moon now is thoroughly awake. Even the 'tired old bird' is fully awake. And its stomach is bulging with the new life.
In the 5th glyph there is a sign showing that the 'flame' downwards is bigger than the others (and also bigger than in all the other seven periods). I cannot see its full significance, but I am certain that it has something to do with the diamond-shape, which also - I believe - is connected to the triangular shape.
And the gods, atua, seems to be gathering (glyph no. 8) in expectation of the coming Full Moon. We now are in a period of tapu.