Depends on the philosophy behind his magic.
Some forms of magic are simply there, waiting to be tapped, such as via sympathetic magic. In which case, he could build something mechanical, driven by normally mundane forces, that is a simulacrum of a natural process associated with magic. (Say, a plasma discharge tube, if the locals believe that the aurora borealis improves magical potency.) In which case, the magic being absorbed is second hand, created by the belief of the local practitioners, but induced artificially through science. In a world where magic has measurably real effects, you can create experiments to measure the thresholds of those effects, measuring all mundane inputs, measuring the energy of the output effect, and extrapolating the energy difference as the magical component. In this way he could quantify magical expenditure, even if his numbers only apply to himself.
The issue that you seem to be having problems with is that magic is ultimately "created" throu 3 unquantifiable sources: faith. Belief. Willpower.
In the case of gizo-x, he has none of those himself, excepting perhaps a loose definition of willpower. He doesn't have faith, because faith is the trust in thruthfulness of a relationship without evidence. He doesn't really have belief, because he doesn't have illogical convictions. He might be said to have willpower, because he doesn't suffer mental fatigue, and is self directing.
His magic is "second hand", in that it relies on the belief other practitioners have that a certain invokation or process will yeild a magical result, which can be shown to be experimentally interesting. He can then perform said ritual, and because others believe it will work, their belief powers the spell. He still has to control that second hand magic though.
It sounds like his G-core power collector absorbs this energy, and is built on borrowed concepts, which is why it works.
His magic could be negated if a sufficiently cynical bastard absolutely refuses to believe he could do magic is present when he tries.
That would change if weird created a "dark core" for him though. It would not have been created by gizo-x, and relies on the will, belief, and faith of my char, and his (very) dificult to deny divine hotline powers. A way weird could give gizo-x such super powers would be say, a mechanical table-flip controlled programmable sigil glyph, tied directly to gizo-x's processing system. Gizo couold manipulate the (absurdly powerful) sympathetic magic construct weird made for him, by controlling the rotation of the concentric rings that the programmable power circle is comprised of, and the tablet flipping controls to alter what glyphs are shown in the circle, and perhaps any other programmable features, like lines, etc. Given a sufficiently in-depth education on the meanings of such reorientations and representations, weird could turn gizo-x into a mechanical "almost necromancer." Gizo-x doesn't have a soul, and therefore couldn't control dead bodies. He could tap all the chaotic magical energy, and use the sigil controller to direct it into other ways though.
He and weird would have to collaborate on that though.