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Hmmm, It is a mystery indeed! Here's what I do know: It looks old, before 1940. It appears to be wool, and the two color weave/weft isn't a weave, at least I'm pretty sure it isn't.
What I don't know: I think, (not positive as linens/fabric/cloth are not my strong suite, and native American items are extremely specialized) that instead of a proper weave we have a hooked blanket here instead, ie like a hooked rug/carpet. The design may or may not be a Native symbol. (You might want to start there, and try to find a similar or identical symbol and see where it takes you). And the colors are unusual. Green and gold, far as I know would not be Native American per se. Especially the Navajo, as they are the traditional blanket weavers. If memory serves, I think their color pallets don't really have gold, and I'm not sure on the green either.
I copied a close up of a Navajo blanket weaving for you to see. (below) Compare it to the way in which your blanket/rug is done. They are not the same. I think you need to find blanket/rug/textiles people to help you, in order to establish if 1. the piece is Native American or not. 2. Is it woven (by hand or commercially) or is it instead a hooked piece, like a rug/carpet would be. Once you have answers to those questions, then it will be a bit easier to figure out exactly what you have here. It's cool, regardless! Good Luck to you!