What kind of religion would develop around a god whose existence was well known, but whose behavior seemed random?
In the scenario I'm thinking of, this god's behavior only seems random - there is actually a good reason for him doing what he does, but it is pretty much impossible to tell what his reasons are. For example, imagine throwing a rock a certain way, causing a moth to change it's path in just the right way so that 5 minutes later it will get eaten by a bat that will then poop on a woman's head, causing her to go to stop at a nearby well and wash it off and get a drink while she's there. No longer thirsty, she does not stop at a well closer to her home from which she would have gotten cholera and subsequently died. Had her son lost his mother, he would have grown into a Hitler figure and caused a devastating war. So throwing a rock prevents a massive war.
In short, this god is very good at utilizing the butterfly effect. For all intents and purposes he is omniscient and omnipotent, so he can do anything he wants do. Also, even though he could accomplish everything with well-timed rock throws, he likes occasionally doing more flamboyant things like showing up surfing a wave of lava pouring out of a volcano.
Some more examples of the kind of things he might do:
- Physically manifest himself to a believer, blessing them with a salt shaker that is never empty for them but always empty for anyone else.
- Physically manifest himself to a staunch non-believing baker, using a penguin-wand to bless them that their loaves of bread will always be twice as large but shaped like a random mammal.
- Curse a believer with feeling like the sky is down every 5th day from 11:05 AM to 11:13 AM.
Some things he hasn't done:
- Overtly interfered with the development of the religion
- Given explicit commandments other than basic moral rules
- Explained what his plan is
He's shown up enough with a consistent appearance for everyone to agree he exists, but because he has neither blessed nor condemned the religion(s) that developed, there are believers and non-believers in the sense that there are people who do and don't belong to the religion(s).
So what would the religion that naturally develops in this situation look like?
As for the basic moral rules, I mean things like "don't murder", "don't steal," and "be honest." I don't have the specifics nailed down, and I'm having trouble thinking of a way to summarize them other than "don't do anything clearly bad." Also, this god is more interested in the spirit than the letter of the law - using legal loopholes/shenanigans to take everything someone owns is still going to count as stealing.
As for enforcing the basic moral rules, I'll say that yes, he does enforce them sometimes. Creatively. There's a legend floating around of a man who murdered his neighbor and was then turned into a lizard. If his legs were pulled off in a specific order and then thrown into a pot of boiling water for five minutes, he would pop back into human form (with limbs intact) for the rest of the day (retaining all the memories of being a lizard, including the process of being turned back into a human).
When he gave (and if he ever has to give again) the moral rules, he did tell the people that they in particular and society in general will be better off if they follow them.