Seager in The ‘Intrinsic Nature’ Argument for Panpsychism names Descartes as the originator of the idea that mental is intrinsic. The most common descriptions of "intrinsicness" single out those properties that a thing would have when alone in the universe, or that any of its "duplicates" would have. Relational properties are the opposite of that.
"The realization that states of consciousness are intrinsic properties is of great
significance. Although he did not use this language, I think Descartes was the first person to argue for this thesis. His skeptical worry that it was impossible to tell
whether or not he was alone in the universe on the basis of the contents of his
consciousness clearly suggests that my duplicates – even if the only thing in the
world – would share all my states of consciousness. The philosophical problem of
the external world and the coherence of solipsism entail that consciousness is an
intrinsic property of things. We do not have to embrace Descartes’s dualism to
share this insight."
This should not be surprising considering his role as initiating the "inward turn" of modern philosophy, with prevalence of introspection, subjectivity, reification of the mental and the possibility of solipsism that comes with it. It created exactly the kind of context that eventually led to the subject/object divide, attempts to overcome it, and the problems with weaving consciousness out of matter as we know them today (the explanatory gap). However, if Descartes counts then I think so should Avicenna with his Floating Man argument, which is indeed often likened to Descartes's cogito:
"One of us must suppose that he was just created at a stroke, fully developed and perfectly formed but with his vision shrouded from perceiving all external objects – created floating in the air or in the space, not buffeted by any perceptible current of the air that supports him, his limbs separated and kept out of contact with one another, so that they do not feel each other. Then let the subject consider whether he would affirm the existence of his self. There is no doubt that he would affirm his own existence, although not affirming the reality of any of his limbs or inner organs, his bowels, or heart or brain or any external thing."
We can, perhaps, push it even further back, to an ancient champion of introspection, sometimes named as Descartes's source for the cogito, St. Augustine, although that is more tenuous. From On Trinity, X:
"But since we treat of the nature of the mind, let us remove from our consideration all knowledge which is received from without, through the senses of the body; and attend more carefully to the position which we have laid down, that all minds know and are certain concerning themselves... who ever doubts that he himself lives, and remembers, and understands, and wills, and thinks, and knows, and judges?... Whosoever therefore doubts about anything else, ought not to doubt of all these things; which if they were not, he would not be able to doubt of anything."
As for the intrinsic nature argument Seager names Leibniz as presaging it, or at least supplying a crucial premise, the thesis about reducibility of relational to intrinsic:
"Leibniz’s panpsychism stems from his view that only mental features have the right
characteristics to perform the reduction of the relational to the intrinsic. Essentially, it is only via mental representation that an entire world can be wrapped up inside a single individual so that all the relations can be ‘read off’ the intrinsic properties of that individual... Strawson does not endorse the Leibnizian metaphysics, but the intrinsic nature argument he advances has interesting affinities with it. One question is to what extent Strawson has to endorse PRR in the extreme form stated above. It may be that a weaker or circumscribed version will suffice for his argument."