This video shows a final (or additional) step in polishing processes. Please note that all the carving of the hair including the bun (after part 3 of this series) and polishing of the entire piece are already done (sorry that those processes were not recorded).
The purpose of this step is to bring out the gloss using tsunoko (baked deer antler ground into a fine powder). In the video, the gloss is not so obvious at first, but around 1:44-1:46 you can see the left side of the face (which is your right side) is shining.
My father uses a high-quality tsunoko given to him by his master and father, Komada Ryusui.
My father carries out this step using his tsunoko on almost all his works. He feels that the same kind of attractive gloss cannot be achieved with modern tsunoko and alternative (chemical) abrasives.
He says that an alternate recommendation is the use of a piece of cloth (made of 100% silk or cotton) that has been washed, without applying anything like oil. Cover/wrap a work with the cloth and gently rub just the high parts to gloss (recessed areas should not be touched/rubbed). To do this, the work has to be well polished in advance.
Incidentally, he has carried out this step since he was more like a craftsman than an artist, in order to make his works look better.
In this video, my father also talks about brushing in regards with gloss. The point is to bring out the gloss on highlights and not to do so on recessed areas, thereby enhancing three-dimensionality.