Thanks @jhgoforth. I’ve been struggling with this too. I made a list and invented my own formula. It’s got exceptions but that resource has explained the exceptions for me.
にん and じん according to my forumula
- じん has a dakuten. That is, it is じん not しん.
- にん has no dakuten.
- When looking at a word with 人, look at the other kanji.
- If the other kanji reading begins:
a) with dakutan, use にん e.g. にんずう 人数
b) without dakutan, use じん e.g. さいじん 才人
Here I have listed examples from my notes. I used blue highlight to describe the exceptions.
Note that all にん exceptions are “occupations”: villain, merchant, chef, witness. Amongst the じん exceptions: べつじん (changed person), which would fit into that “attribute” category in the article. Apparently, soldier is not an occupation ぐんじん.
My Japanese housemate said that she could tell which one to use because the other one would make the word harder to pronounce. It is different for native speakers. 