Citations for Purported Echo Abilities

[Vyrerus]

Uhm, there's a few fights with the Scions... think it was Alphinaud at one point? They say something like, "I can sense the aether swelling. Get ready for an attack!" Then a group stack AOE marker goes out. So it's something that can be sense by people who can manipulate aether or any magitek device that detects aether as well, as far as AOE markers go.

The Gladiator questline has Aldis remark on, "watch how she fights; it's not exactly high theater." or something like that, so there's also the physical reading that we do.

As far as the Echo buff in combat goes, it's most comparable to the Blessing of Light received from Hydaelyn during the Ultima Weapon encounter. Basically, you're supposed to be destined to beat the fight, so your power swells up with the Echo. But this buff is also implemented by the devs on old raid content automatically without any wiping required for things like Binding Coil and Savage Alexander and such.

In theory, if we could control the Echo, then we could use it to view the past of our adversary to see exactly how they fight and to know all of their moves, since viewing the past is what our Echo does. Of course, not all of our adversaries are combat veterans, like Tsukuyomi, so it's not really for reading moves. I coulda sworn though, that there was an aspect to it that made Echo blessed individuals more proficient in combat. Better able to sense aether swells and things, maybe?

[Jandor]

Again, gameplay and story segregation - it's a gameplay mechanic given a vague lore term simply to make it interesting but has absolutely zero connection to the actual narrative (it's also pretty telling that the 'Echo' buff was changed name wise to 'Brilliant Conviction' in many battles that had the mechanic, as if SE themselves are basically stating "uh, no, sorry guys, this actually has no connection to the Echo at all, sorry for misleading you"). Basically, it's just the game's way of saying "You're the Warrior of Light and you're going to kick ass here".

This strikes me as more a gameplay mechanic with a bit of flavor than an actual lore thing.

I know it's primarily a gameplay thing guys, the OP asked if there was a citation & that's the closest thing I can think of to one.

I do enjoy that the devs give these sorts of things little fluff justifications though, it's not relevant to the main narrative and it's essentially not really important if it's actually canon or not, but it is nice for those that enjoy some sort of in world justification for the gameplay.

[Alleo]

This strikes me as more a gameplay mechanic with a bit of flavor than an actual lore thing.

Seeing how the kinda made it a big deal that Mikoto was able to get a glimpse of the future with her echo I agree that its more a gameplay mechanic. Otherwise the WoL would have a much better future echo than anyone else which would make it even worse when we are taken down or react to slow to things.