from typing import List
import heapq


def find_nth_highest_index(input: List[int], n: int = 2) -> int:
    """
    Finds the nth highest item in a list and returns its index.
    Note that n is 1-indexed here, e.g. n=1 would return the 1st largest element.
    """
    heap = []  # Create a min-heap of size n.
    for idx, value in enumerate(input):
        if not heap or len(heap) < n:
            heapq.heappush(heap, (value, idx))
        elif value > heap[0][0]:
            heapq.heappushpop(heap, (value, idx))
    value, idx = heapq.heappop(heap)
    return idx