Not every monster is a mix of a bunch of Apostles, it most likely is a direct first born of the 1st or perhaps a second born, regardless literally the ONLY real ability is Perception, not Desire. We know Jake can issue commands so far as to make you think the person in front of you is your son, replace information, etc.
I've talked about this before. Authority does not change perception. It changes behavior.
For Jake's power to be about perception, he would have to alter how you see him. He can't do that.
His powers literally stop you from thinking the things that he doesn't want you to.
He hates that he was fat, so everyone can't remember that he was fat but people still can perceive that something changed about him.
He is afraid of MC finding out he is a s/h, whenever MC tries to reach that conclusion he gets a headache or he forgets what he was tlking about.
MC doesn't have trouble perceiving Jake for what he is. He has trouble acting on these thoughts because Jake doesn't allow him to.
When Jake commands MC to stay in prison, MC feels that (quote) "his desire to escape, vanished entirely". Since he can't act on his desire, his feelings change and he feels that prison is his home, till he breaks the command, becomes able to act on his desire to leave the prison, and he stops thinking that.
We also have strong indications that Jakes power would be able to affect objects.
Objects don't have perception. They do have behavior though.
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When Jake imprints Deryl, Deryl ends up falling in love with Ella. He feels that she is his world, that he wants to protect her and prove to her that he is the only one she needs.
This is, point for point, the exact behavior Clover has when Demi infects her by mistake.
Clover perception is not altered. When Demi tries to undo the effect, Clover knows what she has done and begs for Demi to not undo it, otherwise she won't be able to live with herself. If she had altered perception, then she wouldn't be able to say that. She would be confused, like a schizophrenic who commited a murder by mistake, because he perceived something different than reality.
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On Demi's possible connection to 4th and 8th.
Demi
doesn't know what her target sees when looking at her illusion. This means that whatever she creates has to do with the individual. Of the Apostles that we know, only the 4th has the capacity to read an individual and act on it (4th reads MC's memories and turns into a chick to blow him).
If Demi knew what her target saw, then we could easily say that she made the target think that. But since this is obviously wrong, her trick is an actual visual illusion. Illusions are tricks of light so here's the connection to 8th (assuming ofcourse that 8th is light).
So she could have some bastardized power that is the combination of light and memory which creates these effects. My money would be on the 1st being the primary influence on her powers, but the other 2 are also plausible. In any case, "Desire" is the perfect way to explain her powers. She can turn into an object of desire, or force her targets to see the object of their desire.