The concensus on what I've read is that you must have unlocked it (beaten Crota on HARD at least once before), but don't have to have it on or in your inventory.
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Got glowhoo on my first hard Crota completion a few days ago. Would I need to wait for the raid rest for a chance at the crux?
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I'm not sure, but I think so. I'd be happy to be proven wrong as I'd like more than one shot /character /week.