The first two lines of step 8 of the glaze instructions don’t make a whole lot of sense. Is the caked glazed while warm or cooled completely?

The cake is warm when glazed. Sorry for the confusion.

It does say to "cool to room temperature" after glazing, so presumably it's still warm, I think just the 15 min. cooling suggested- it will certainly penetrate better in a warm cake. I'd go with grandma and use the toothpick, too- it really helps, and the holes generally swell most of the way closed and present no problem.