The bestiary entries for Light and Shadow. Basically, the rabbit on/in the moon is a myth that, while it exists in basically all cultures, is also Chinese. The owl has many associations with death in Chinese and a rabbit is always good luck, plus the two play a nice predator/prey role that I think goes well with the cycles of the moon.
If you want specifics, you can read the pasted entries
Moon Rabbit
The Moonlight Rabbit is native to Northern Keihatsu territories and shares no counterpart to the Sunlight variant, as their fur can only be seen under the reflected light of the moon. During this time, the Shadow Owls relentlessly hunt the Moonlight Rabbits, with the success of each dependant on the moon’s phases. The bright sheen of a full moon prevents them from being attacked as it blinds the Shadow Owl, and the dark of a moonless night not enough to protect the Moonlight Rabbit from the Owl’s impeccable sight.
The Moonlight Rabbit is a rare sight to humans, however the trickster nature of younger Rabbits can lead people to stray from the safety of their homes at night with many going crazy at the game. Upon aging and gaining wisdom, a Moonlight Rabbit can be a sign of fortune and good health as they will sometimes do what has been described as “light-stepping,” in which they will temporarily solidify light particles to allow them to continuously jump. The particles turned to platforms then become dust as soon as the Rabbit loses physical contact, which then sprinkles down onto crops and on the ground. The powder lasts until morning, when the sun’s rays absorb it, but can be collected and used for medicine.
Shadow Owl
Native to Northern Keihatsu territories, the Shadow Owl is a notorious and prolific hunter that will silently stalk both people and its prey: the Moonlight Rabbit. The Owl’s feathers are colored so darkly as to blend into the moonless, starless night that the presence of a full moon makes them significantly easier to spot against the bright light of the moon by the Moonlight Rabbit, who also rely on their hearing during times of complete dark.
To the Keihatsu, the Shadow Owl is a terrible omen, one often laden with themes of death. Their ominous “hu” means to dig a grave to the culture, and it is said that they only leave the nest after pecking out the eyes of their mothers. The Owls themselves have proven to be associated with a following disaster or tragic event for individuals whom they stalk, however the Owls become visibly restless and loud when such events approach.
Duality
The Moonlight Rabbit and Shadow Owl represent the powers of night within the northern Keihatsu territories, with shadows being most prevalent in the absence of the watchful moon and stars and the soft light prevailing under the eyes of the night sky. The Moonlight Rabbit brings good fortune and health to those able to harvest the powder produced by a Rabbit’s light-stepping while the Owl is heavily tied to themes of tragedy and death, often of great illness and pain.
(I put Northern Keihatsu since I see those areas as being more representative of East Asia, so China, Korea, and Japan, and Southern Keihatsu as Southeast Asia, so Indonesia, Vietnam, the Philippines, etc.)