I can remember as a little boy that my brother and I each got something like what you have in your picture from our parents were traveling through New Mexico ? The narrow end was the top and the wide end was the bottom. The larger sections on the front was turquoise with the thin bands being silver or silver color. They were used in this type of rope neck tie. May not be what you have, but looks an awfully lot like them. The hook went over the top button and in between the collars. This was the closest thing I could find that could give you a visual image of what it may be.
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