The time zone regulation describes the line this way: "From the junction of the western boundary of the State of Michigan with the boundary between the United States and Canada northerly and easterly along the west line of Gogebic County to the west line of Ontonagon County; thence south along the west line of Ontonagon County to the north line of Gogebic County;"
But this description doesn't seem possible, because Gogebic County doesn't border Canada:
It seems that the zigzag line on the map was their attempt to follow the description anyway.