As mentioned in the new rules post, I have been given the task of learning about Jiin in order to be able to fact-check K's kata research during his kata test. So here's what I've discovered...
The kata's origins are mysterious - which isn't unusual, but there is even a dearth of mythical origin material. I had to really dig around in my books to find some bits and pieces. It is well-known that Jiin (sometimes Ji'in) is grouped with Jion and Jitte (sometimes Jutte), not only because they all begin with the Chinese greeting of friendship (the right 'fighting' fist covered by the open left hand, sometimes called the Ming (明) or sun-moon greeting), but also because they include a lot of the same or similar techniques. Indeed some believe the three kata to be derivatives of one single forgotten kata.
In a 1914 Okinawan newspaper article, Gichin Funakoshi, recalling his teacher Azato's words, claimed that Jiin was taught to the Tomari-te teacher Gikei Yamazato (1835-1905) by a shipwrecked or stranded Chinese martial artist from Annan. This man also apparently taught the kata Chinto (Gankaku), Chinte and Jitte to various Okinawan karate experts.
The Shito Ryu and Itosu Kai sensei, Ryusho Sakagami (1915-1993) believed that the three 'J kata' were Itosu's reformulation of older Tomari kata, since lost. Itosu was the creator of Bassai-sho and Kanku-sho, and some karate practitioners see Jiin as a kind of Jion-sho (Funakoshi, in 1925, said that some of the kata were derivative, resulting from changes made to other kata, so that may have been a traditional practice - unlike today where forms are very much set, with deviation frowned upon).
The name itself, Jiin, is also subject to confusion. If the kanji 寺院 are used then the meaning would be something like 'Buddhist temple' or 'temple grounds'. If the kanji 慈陰 are used then the meaning would be something like 'hidden, or secret, mercy'.
In his 1925 book, Rentan Goshin Karate Jutsu, Funakoshi mentions Ji'in and like many of the kata at that time, its name is given in katakana (ジーン) rather than kanji, suggesting only the sound of the name was known (interestingly, an online translation gives a definition of these katakana as 'heartwarming', 'deeply moving' or 'strongly emotive'). Later, Funakoshi tried to rename the kata to Shokyo (pine shadow), but unlike many of his other new 'Japanified' names, it didn't stick. It is not one of Funakoshi's core fifteen kata, though he does mention it as one of the forms being taught at the Shotokan as of 1943.
In the end, I think it is safe to say that Jiin is a kata with a strong Chinese ancestry, probably filtered through a Tomari-te lens, and introduced into the modern age via Ankoh Itosu and his students.
One last point of interest: the Shotokan version of the kata does not include the final four moves found in other styles (eg. Shorin Ryu, Shito Ryu). These consist of an age-uke followed by an oi-zuki, then repeated in the opposite direction. Whether this is a deliberate omission or a mistake in the teaching of the kata at some point, is unknown, but whatever - it has become the Shotokan Jiin.