On the subject of Shun... Tokimi does state that Shun DIDN'T become an Eternal himself, rather his body (which was completely taken over by his sword) became an Eternal. Note that Oath CHANGED to World at the same time. Plus he didn't leave the world, just relocated himself.... Furthermore, touching the gate in the Labyrinth of Time IS what causes a person's existence to be wiped from non-Eternals.... And Shun (his body anyways) never touched it, or for that matter, didn't even leave the world.
So technically speaking, if an Eternal touched it by mistake, it'd affect them AGAIN, thus rendering time rewinding useless if that happens. This is lightly mentioned in a easily miss-able phrasing (during the scene at the gate).... Which means the person/thing at fault in this case is Wisdom, since he was BORED.... remember, Eternals and Eternity Swords aren't affected by memory changes themselves (its everyone else)....
As a result, if a mortal FAILED to become an Eternal after touching the gate, they're well... doomed. Since they have nothing left, literally. This is also mentioned in a completely different way... I just rephrased it in my own words.
And Eternals being forgotten when they leave a world CAN be undone through rewinding time, which is done by Tokimi, otherwise it would have complicated matters. But the gate's effect blocks any tampering by rewinding time of those affected.... which supports the above statement, since if Tokimi had accidentally came into contact with the gate, rewinding time would NOT reverse HER being forgotten due to leaving the world.
Oh and in regards to him remembering her despite him being in a DIFFERENT world than her (for most of the game/story), note that HE left his world (abit forced and not willingly), while she was STILL in his (or rather their) world. And since she came to the SAME world as him, he is NOT affected in the least. Of course this applies to the other three as well.
So technically it IS possible to remember an Eternal if you're one-step-ahead of them in leaving the world. But if they EVER leave the world you're in BEFORE you, you WILL forget them completely. (Well except if someone is kind enough to undo the wipe when said Eternal you knew is in the same world as you again).
Its pretty consistent throughout the various routes if you take all of the above into account, and not generalize Yuuto's case for EVERY Eternal. The below makes sense and runs off the previous statement in one-upping Eternals.
Well actually, what happened was:
-Yuuto and Aselia leave Phantasmagoria
-Takios and Temuorin leave Phantasmagoria so everybody in Phantasmagoria forgets them
-Yuuto and Aselia return to Phantasmagoria
-Takios and Temuorin return to Phantasmagoria so everybody in Hyperia forgets them.
-Thus, the conclusion is that Yuuto+Aselia did not forget them
And.... thus its safe to say that, if you end up in a world that the Eternal (that you know, of course) doesn't come into, you'll remember them until they end up and leave the world you're in. Or if they touch the gate in the Labyrinth of Time. So basically the memory erasure CAN be averted/subverted, while alterations caused by the gate, is NOT undo-able/stop-able if you touch it at all (Eternal/Eternity Sword/Mortals/etc.)
Edit: And for the record, she tries to outright avoid what she doesn't want to answer (note the bath scene..., on her route of course) or simply speaks very very vaguely about it, or if that's not possible, generalizes it, or else (abuses) her power to evade the question altogether (the aforementioned bath scene is an example of the last one). For best results in dragging answers that Tokimi's that vague about, or avoids, Temuorin is quite effective at that....
So technically/literally she's not a liar, just very difficult to get certain information out of her, but still highly possible. Oh and... she can't fully predict what will happen in regards to Eternals, but can narrow it down based off what she knows, so it is possible to take a wrecking ball and shock/surprise her. Or if she's distracted it'll have the same effect... ditto if she's not thinking straight at the time.
In which, its quite amusing to consider her as a manipulating woman towards Yuuto. Its rather he's... an idiot, since Tokimi DID explain her power to him... yet Yuuto fails to realize the faults in her power (or the abusive potential). And some of Tokimi's actions are as a direct result of taking Yuuto's NEARLY guaranteed responses into account (then and there at the time of course), which is why its easy to say she's a manipulating woman... since she has no ill will towards him... except some parts of his personality (aka thick-headed-ness towards those attracted to him), that result in drastic action (aka the 'eligibility' part). Note, I am not saying she isn't a manipulating woman, just not one in the negative context.