I just finished watching the movie, The Assassin. In it, there is a guy whose job seems to be travelling between villages, polishing mirrors. It seems to be a pretty superfluous occupation, since I can't imagine polishing a mirror would be that specialized, especially for rural villages. Were there actually professional mirror-polishers at any time in ancient China, what exactly made their services desirable, and was that usually their only occupation?
Mirror polisher was a profession in China from ancient times through to the 20th century. The traditional Chinese mirror was bronze (typically a very high tin bronze with some lead for improved castability), usually circular, decorated on one side, and the other side - the reflecting side - polished smooth.
Bronze mirrors like this appear in China quite early, with some examples supposedly from the early 2nd millenium BC, and they are mentioned in texts as early as the 7th century BC. They were initially luxury items, but became much more common during the Han Dynasty.
Since bronze tarnishes, such mirrors need to be re-polished frequently. Since the polish needs to be fine (for a smooth surface), and the mirror surface must be kept as flat as possible, this polishing was usually done by professionals. Mirror polishers even had a patron saint, Fu Ju Xiansheng (負局先生), a Daoist immortal who had worked as a mirror polisher.
Finnane (2016) notes that in 1923, traditional mirror polishers were still working, but had become very scare (traditional mirrors having been largely replaced by modern glass mirrors). Finnane further discusses ancient and more recent Chinese mirrors, and artistic depiction of mirror polishers.
References:
Antonia Finnane (2016), "Folding fans and early modern mirrors", chapter 19 in Martin J. Powers, Katherine R. Tsiang (eds), A Companion to Chinese Art, Wiley, 2016.
Liexian Zhuan ("Biographies of Immortals") on Fu Ju Xiansheng (in Chinese): https://ctext.org/lie-xian-zhuan/fu-ju-xian-sheng
For more on Chinese mirrors and their optics (pp 87-97): Needham, Joseph and Wang Ling (1962), Science and Civilisation in China, Volume 4 Physics and Physical Technology Part 1: Physics, Cambridge University Press.