The DT Extractor's purpose and use (pre-Alphys)
The machine in the True Lab has always fascinated me, because it is clearly not built by Alphys. Skull imagery is not once associated with her other work, and its uneasy design doesn't feel like something she'd pivot towards in the first place, especially since it was meant to be a simple extractor. We DO know of a previous scientist who enjoyed creating that sort of machinery though...
I think the implication is clear. The machine we see was built by Gaster long before Alphys took his place. She herself says she "used the blueprints" to do what she did, implying she was following a pre-existing base during her experiments.
People are still confused about Alphys' involvment with the old royal scientist, which leads to the common misconception of the two of them working together in the past. We know this cannot be the case because of Alphys' backstory and how it does not intertwine with Gaster's at all.
Prior to becoming the new Royal Scientist, Alphys was a simple girl who scavanged for trash with Catty and Bratty.
She was not involved with any scientific duty prior to obtaining her current position, outside of helping her friend Mettaton achieve is life-long dream of a body he could love and feel at ease within.
In fact, that deed is what interested Asgore in the first place, as Alphys seemingly advertised Mettaton as a robot she had built, who was powered by a SOUL of her own making.
All of this happened long after Gaster had already vanished, as Asgore could not find a worthy replacement for a large amount of time.
I think Asgore's interest in Alphys and her "robot with a SOUL" stemmed from its similarity to Gaster's previous research.
The one oddity that remains is Alphys and her usage of the word "Determination". She was the one to coin that term, and the extractor is named after the substance.
I think this points to her naming the machine for the purpose that she has for it. I don't believe she lied about coining the term Determination since she is already upfront about the blueprints not being hers. This begs the question though: what was Gaster using this extractor for? I want to say for the same reason Alphys was using it, especially if we believe both of them were researching the nature of the SOUL. Perhaps Gaster simply never named the substance he discovered, or if he did, its name became lost, like the rest of his lab entries and research. After all, Alphys had to reverse-engineer the machine using his blueprints.
The main difference between them would be the revelation Gaster obtained during his experiments. We know from his one entry in Undertale that he discovered the Dark Worlds seen in Deltarune. His description of what he witnessed matches what happens when a Dark Fountain is created.
The power of will, also called "Determination", is what's channeled to open these rifts in the earth. Therefore, it's very possible that Gaster sought that will too, to further his experiments.
However, who was he extracting the substance from? It could have been some of the Human Souls, sure, but that seems to have been a thing Alphys came up with. Perhaps he had a different source for that power... like the monsters themselves.
Now, another misconception is that Monsters in Undertale completely lack Determination, but that is not quite true! Monster Souls are indeed weaker than Human ones, being unable to persist after death. All Souls possess the will to live, however. We are shown this through Undyne, who is a regular monster that holds an incredible amount of Determination for her kind's standards! As far as we know, she is just herself, no enanchment or DT syringe or any of that stuff. This is simply her will manifesting as she dies.
Another instance is found in Boss Monsters, the only species that is comparable with Humans regarding the quantity of DT they possess. Their Soul can persist briefly after death, which, as explained by Alphys, is a result of the substance she discovered within the SOUL.
This shows monsters DO have Determination. The amount they hold is indicative of the strength of their SOUL, but it's a quality inherent of most living beings (with a consciousness anyway, sorry flowers!).
This reading is further supported by Deltarune itself, as Queen believes all Lightners posses that same power, regardless of wether they are a human or a monster...
... and well, they do. Susie opens a Dark Fountain in front of our eyes!
So this is what I propose: the Gaster Followers and Goner characters we meet in the world of Undertale are actually monsters whose Determination was extracted long ago to further his study of darkness and the Dark World. This drastic process drained their being of all color, essentially leaving them as husks. Alternatively it's as Alphys theorized, and their host bodies were completely lost in the process, later reforming as colorless copies of themselves. Because as we know by now...
If your will to exist is all drained, wouldn't you cease to exist completely? This never happens to the Human Souls that Alphys extracted DT from because they have it in large quantities (and draining them completely would be detrimental to shattering the Barrier)... but maybe this is what became of these unfortunate subjects. It may explain why Goner Kid laments their nonexistence, in fact.
This always felt like it didn't quite relate to Gaster as much as people believe. Their plight feels earnest, which doesn't exactly match the way Gaster has been characterized by both his followers and his interactions with us. Though he may not exist in the world anymore, all his inventions are integral for the functioning of the Underground and Undertale's narrative at large. Even his presence seems to be invasive and inescapable, as he is stated to be ALWAYS listening.
Goner Kid's resignation to being forgotten doesn't seem to match Gaster's eagerness for connection with us either.
Their words do fit the tone of a victim whose future has been stripped away, though...
Alphys never tried the machine on monsters because she thought it was too dangerous and impractical, but with everything we know of Gaster from Deltarune, I start to think he wouldn't let such a thing stop him. Heck, it's actually quite believable that he would go a step further and do the same to himself, which may be what led to his shattering and ascension...
After all, we are told that he fell into his own creation... and a very noticible trait of the room we find the DT Extractor in is the dark, gaping hole it rests above. Quite a perfect place to plummet into, wouldn't you think?
Why he would do this? Perhaps it was peering even closer behind the curtain and finding out something he shouldn't have. Perhaps the manufactured nature of his very existence. It's something Deltarune itself seems to be exploring too, after all... or maybe he saw the existence of someone, or something that he could just not live without.
So he removed himself from the equation, and became something grander. Something very, very interesting...
The more frightening part?
Perhaps she was closer to her predecessor than we believed...
