Further evidence all ph wander:
https://web.archive.org/web/20060420....shtml?id=3452
“OoT ancient cyclops
4) Once you are ready to start the spawn/ph cycle for the ancient cyclops (pending that it isn't camped already) you must find which 1 of these 5 creatures is up on the island. Once the mob pops they will wander the island, so if the mob is already up when you get there you must find it (i think it walks over to the west side of the island) and kill it to begin the cycle”
Incidentally this page mentions to be wary of fearing the S Ro version as the dark elf vendors will aggro it (like they do sand giants).