Is it possible that just the same happened to this couple that happened to me in 1982 in Utah? I was a tourist, had a rented car and my car also stopped on the mountain. I waited for a while it worked again. Later when I arrived in a town on the other side of the mountain and asked they told me I hade Carburator Freeze.
With Carb freeze your start motor probably worked. In the case of the Utah mountain Toyota, the starter motor didn’t crank.
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