So after having Cayde's Stash as the Daily Heroic Mission, and specifically that nothing was found on it, I think I have an explanation for both the mystery of Cayde's Stash and the Black Spindle.
Upon finding Cayde's stash spot through the vents on the mission Cayde's Stash and reaching the end, the room is empty, assumed to have been raided by the Fallen. He discusses how he uses the cards to mark locations of weapons, but as there is a card on the stealth drive I would assume the queen is followed by jacks and there were two items he hid here, one being the drive. However, according to the dialogue the hidden weapon is of Hakke design (This particular part of my explanation cannot be confirmed until the Grimoire card is declassified, if ever. Few exotics specify their design origin.).
The Lost to Light mission follows this one, granted with a couple in between. Once you do find the hidden area, where should it be but a Fallen Ketch? Who fills almost the sole ranks and leads the Taken? The Fallen, and once you defeat them you find a great exotic weapon.
It is my belief that the Fallen raided the stash, and were attacked by the Taken. They escaped Earth on their Skiff and retreated, chased, to the Moon o try and reach their Ketch, but failed and were Taken themselves, and you arrive afterwards, just before the Taken leave this realm.
But like I said, this would be much more valid or invalidated if the Black Spindle could be confirmed as Hakke or otherwise.
I have also found some other vents on the Rasputin Mission The Promethean Code, that are inaccessible. However, I feel that may change or alludes to something in a later mission, Last Rites or Regicide.
Anyway if this yields, post something and let us know!
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I feel like there's a way to get back to the sepiks prime fight and we fight a taken sepiks and get an exotic version of another year one gun. [spoiler]probably a vog weapon because of caydes interest in the vault. And also because the spindle was an exotic version of a Crota weapon, which makes me think that they wanted us to discover (if there even is) the secret in caydes stash first because it was one of the first missions in ttk. [/spoiler]