hey hey hi hi! dearest archivist, do you know anything about the Gemini Jester and what it has to do with Daito/Braytech/The Jade Rabbit? I've searched about it a couple times across the past few years and I've found jack squat
First of all, "archivist".... 🥺🥺🥺
And honestly, as far as I know we never really find out! Gemini Jester has the jade rabbit and Clovis Bray symbols, and the former is obviously the Daito mascot. Daito itself is a weapon foundry almost certainly established before the Collapse, considering we can find its logo in Golden Age ruins on Mars and Venus. D1 Grimoire card of The Jade Rabbit states the gun was created from reassembled Golden Age technology, including the casing made from plasteel sourced from a First Light installation on the Moon. Shadowkeep also introduced these little jade rabbit mascots you can collect by giving them rice cakes.
The jade rabbit is a figure from real-life East Asian and indigenous American folklore, born from the idea that the dark markings on the visible face of the Moon resemble a rabbit or hare. According to the Wikipedia page, "Chinese versions, the rabbit pounds medicine for the mortals and some include making of mooncakes" - which might be what the giving-jade-rabbits-rice-cakes thing was inspired by!
Some other pieces of Daito gear (Two-Tailed Fox, for example) reference or are clearly inspired by East Asian culture, the company name is literally a Japanese sword, and their director Chiyoko Mey bears a Japanese name, so it all sort of fits together aesthetically and thematically. There seems to be some thematic connection between Gemini Jester (you know, jester) and The Jade Rabbit, considering the gun's predecessor was literally named The Fate of All Fools (and this is also nodded at in JR's main perk name), but I genuinely can't say much more other than "these two things seem to strike a similar vibe" lol.
Destinypedia theorises that the Clovis Bray logo might suggest Gemini Jester was a collaboration between Braytech and Daito, which would make total sense timeline-wise if you consider the Daito logos in Golden Age ruins and the (probably Golden-Age, because who else would've left them there? unless we wanna jump back on my old theory that the jade rabbits are sentient, which I still wholeheartedly believe) mascots on the Moon. I can't recall any lore that solidly confirms any of this though.