It doesn't take much thinking to realize that the vast numbers of various peoples native to the Americas, had even more varied ways of dealing with their deceased. Was the simplified relationship between those and the paranormal just a lazy grab of the nearest "mysterious" thing by horror writers or was "Indian magic" used to explain the unexplained in the earlier times as well?
King's Pet Sematary (1983) in particular is a near-archetypal encapsulation of the Indian burial ground trope, but its roots wind all the way back through the history and prehistory of truly American (in the USA sense) literature--the strange and wonderful longevity of the American Gothic. The platitude that Europeans left the "enchanted landscape" behind in Europe, bringing to America Puritan and Anglican rationality rather than elves and fairies, is a lie already unmasked at Salem. What they brought was a fear of "wilderness," the land of dark forest=>darkness and the unknown.
Openly religious writing for edificatory purposes permitted factual discussion of demonic possession (of people and houses alike!). But when white, newly-American writers and their audiences incubated the first bestselling Anglo-New World fiction genre--the Indian captivity narrative--Native Americans frequently took on the demonic/fae role. Violent terrorizers, original inhabitants being trespassed, corrupters of women. The central role of place in Gothic lit overall takes on fresh importance in the American wild/erness, too.
Even the sort of "prehistory" of captivity narratives, emerging out of New Spanish chronicle accounts, already absorb European fears over this American wilderness played out through Native Americans alive and dead. In the 1605 La Florida del Inca, a retelling of Hernandes de Soto's war, conquistador Juan Ortiz is captured near modern-day Tampa by a group of Indians (the nation is not noted) and, yup, forced to guard a burial ground. The proto-Gothic themes in the story are perhaps less tied to the burial ground than they will be later in Anglo-Puritan narratives, but the presence of the dead Native Americans is nevertheless highlighted. The bodies are not buried but are kept above ground in wooden sepulchres.
Indian captivity narratives captured the fascination (and book-buying money) of white American readers in New England in the next century. And the narrative role of Indians as substitute-demons led to a smooth glide over the life and death boundary, this world and the next, in American imaginations. Philip Frenau's (you know, the "Poet of the American Revolution" himself!) 1787 poem "The Indian Burying Ground" is one of the most explicit and concentrated assertions of the power of the mystical-otherworldly-demonic Indian tied to the American land in early Euro-American lit:
In spite of all the learned have said / I still my old opinion keep;
The posture, that we give the dead / Points out the soul's eternal sleep.
Not so the ancients of these lands— / The Indian, when from life released,
Again is seated with his friends / And shares again the joyous feast.
[...]
Thou, stranger, that shalt come this way / No fraud upon the dead commit
Observe the swelling turf, and say / They do not lie, but here they sit.
[...]
By midnight moons, o'er moistening dews; / In habit for the chase arrayed,
The hunter still the deer pursues, / The hunter and the deer, a shade!
And long shall timorous fancy see / The painted chief, and pointed spear,
And Reason's self shall bow the knee / To shadows and delusions here.
Moving into the next century and the evolution into Gothic as a genre, the first important author is probably Nathaniel Hawthorne. With a different agenda than the earlier Indian captivity narrative authors (Hawthorne's version of the infamous Hannah Dustan narrative paints her, not the Indians, as the real monster), throughout his corpus Hawthorne adopts and adapts "mystical deadish Indian" themes into Puritan horror, specifically connected to the perpetrators of the Salem witch trials. Hawthorne's direct heir in this very specifically New England horror/Gothic is of course Lovecraft, whom /u/AncientHistory is probably more qualified to discuss than I.
Scholar Renee Bergland (whose overall interpretations I don't always agree with, but who traces the literary history and influences very nicely) follows what she calls the "spectral Indian" through the nineteenth century. The U.S. government's repeated and violent encroachment on whatever land Indians happened to be residing on, the repeated and violent expulsions to the west, left behind their "ghosts" in white authors' imaginations. They remained rooted in the landscape--less now because of their earlier role as replacement fairies and more because of the immense shadow that land/place occupied in the American literary imagination.
For Stephen Bruhm, King's use of the Indian burial ground trope is strongly "New England" not just in its geographical location but in his repeated return to children as the nexus of horror. Children are the other great wilderness in predestination-soaked Puritanism--they appear so adorable and good and innocent, but some of them are destined for hell. Those reprobrate are indistinguishable from the others: they are demons in disguise, the most terrifying demons of all. To King (well, his characters), the anxiety parents raising children in light of death tracks with the white American view of the ephemerality of Native Americans--the ephemerality disproven by the mystical staying power of the burial ground:
They stayed here in Maine for a thousand years, or maybe it was two thousands--it’s hard to tell, because they did not leave their mark deep on the land. And now they are gone again...same way we’ll be gone, someday. (Pet Sematary)
(Edited: formatting)