All right. Time for another postulation on background on Ten Desires.
There is a religious practice in Japan that is called "Shugendo". It is a mixture of "Japanese Native Faith" (TH10), "Shinto / Taoism" (Reimu), "Buddism" (TH12) combined together, became popular during Heian period.
The principle of this religion, as far as I understand, is to combine the principle of Taoism / Shintoism (Reimu) and the reincarnation/enlightenment (TH12) concept through reverence, worship and discipline in the mountain (TH10). The followers of Shugendo is called Yamabushi(山伏), or "one who worships the mountains", whom are known in the folk legends of Japan as those who have powers to "summon gods and holy spirits" to exorcise evil spirits (youkais) (or another method is to make shikigamis from the defeated evil spirits to fight another evil spirits, which will explained further later). These Yamabushis, like their name suggests, dwells on the mountains and seek for oneness of man and nature (Japanese Druidism of the sorts).
A man who is the most famous, who is also the founder of Shugendo, was called En no Ozuno (役小角) / En no Gyoja (役行者) , venerated as Jinbenbodaisatsu (神變大菩薩), who has become a subject of legend of Japanese asceticism and mysticism. (as a bonus, he was referenced in Ran's Spell Card in STB (8-7) ), Two of his famous summons (or Shikigami) are simply known as "Zenki" (前鬼) and "Gouki" (後鬼) [For those who remember, this was Ran's Spell card in phantasm, also what Yukari called her crows in SSiB, so it's probably a very generic term as the name Zenki and Gouki's literal meaning suggest). He also had a guardian buddha that only exists in Japan called Jauogongen (藏王權現), who is a representation of Power of Destruction.
The mountain that is highly associated with Shugendo is Mount Yoshino, where it is said that En no Ozuno meditated and disciplined. The place is famous for several things, including the phantasmagoric scenery filled with cherry blossoms as En no Ozuno revered Cherry Blossoms as a symbol of Jauogongen - potential tie in to appearance of Youmu (TH7, PCB) (also liked by many famous historical figures in the future like Toyotomi Hideyoshi). The place is also erected with a temple (金峯山謝), where there's a little shrine in tribute of its Shintoism.
Like many other native faiths and worships other than Shintoism, Shugendo was banned in Meiji era in 1872. After 1945, the revival movement of Shugendo followed, but by that time, it was a modern era where Shugendo is only considered as a gimmick rather than a something to be fully devoted or considered as a religion (a very fitting setting to be entered into Gensokyo).
And thus concludes my own summary of Shugendo, and by reading it, it has a nice tie ins towards something that ZUN will heavily reference in TH13, and potentially summon some characters according to Shugendo legend. Like JoJo, ZUN might reference Zenki (鬼神童子ZENKI), a manga and anime series in 1997, where shikigami Zenki is freed from En no Ozuno (also making an appearance in the series) and does all the anime stuff settings (fighting evil demons despite himself being an evil demon, etc. etc.).
I am still wondering how this ties in with the title Ten Desires, but it probably has to do something with the Buddism part of Shugendo and the ten different levels of enlightenment (from heaven to hell, pretty much).
