The one inside the Deku Tree is story-relevant, so I wouldn't be surprised if that one was specifically programmed to NOT respawn. It would be weird for the Deku Tree to fall ill over and over again just because the sentient ulcer inside of him frequently reappears.
All others I've found so far seem to regularily respawn tho. If you want to know where their locations are, you can use this map and just scroll all the way down to the "Gloom Spawn" button.
(IIRC it is somewhat random what equipment the Phantom Ganon carries, so it might make sense to savescum until one with a sword shows up. I'm not 100% sure aboutt he randomness tho as I usually avoid those things if I can help it.)
Isn't the equipment fixed. I also saw one on the way through the korok forest depths and not in the tree. It didn't respawn either. That or I placed my pin bad
I heard it was allegedly random, but like I said; I can't really verify it as I've been avoiding these Eldritch Horrors whenever possible ^^° Might just be a rumor then. I can test it later tho if you'd want me to.
I've done it so many times I know it stays same. Citadel and faron forest have spear ones. Between gerudo and far on there is a club. In hyrule castle chasm their is a spear one. Another club in spring of power i think.
Gloom weapons are decent till you get late midgame loot
Update: The one in the Maritta Exchange Ruins (coordinates: -1781 | 1682 | 0107 according to the interactive map) dropped a Gloom Sword for me right now.