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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Not too sure, at the end of the story, Cayde's stash, when you scan the guardians box, it says the number as 10201. Near the bridge, on the control panel, the card is a queen. In the secret room, its a jack, and at the end, near the stealth drive, i think its a king. And when first u step on the elevator, cayde asks ghost to standby and resurrect; so after we killed the echo, we tried to kill ourselves. On our surprises, some spawns bought us back to the control panel. But again, we havent find anything just yet.