As Jeeqbit said, Eulmore's aetheryte unlocks after you pass a certain point in the Main storyline for ShB.
There are incidentally a couple of other examples of non-functioning or locked aetherytes in the game though - as just some examples,
the aetheryte in the Doman Resistance headquarters in Yan'xia in SB is locked for a while until it's repaired, and at least two aetherytes in certain areas of EW (specifically, the main aetheryte for Radz-at-han in Thavnair and the aetheryte in Tertium Station in Garlemald) are also locked until you pass certain points in EW's story,
so there is precedent.
So if you come across an aetheryte that won't let you attune to it yet, usually it's because it's unlocked eventually later on as part of the main storyline, usually due to lore reasons.