Gave it another shot:

    def monotonic(arr):
        if not arr: return []

        new_arr = []
        sub_arr = [arr[0]]
        parity = 0

        for n in arr[1:]:
            delta = n - sub_arr[-1]
            if parity == 0:
                parity += delta
            elif parity * delta < 0:
                new_arr.append(sorted(sub_arr))
                sub_arr = []
                parity = 0
            sub_arr.append(n)

        new_arr.append(sorted(sub_arr))
        return new_arr

`delta` keeps track of whether the next element increases or decreases, whereas `parity` keeps track of the parity of the run. No imports, arbitrary iterators, single function.

You can continue to pare it down.