"""Parses a response string into a list of keywords, applying fallback rules for formatting.

This function processes a multi-line string response, extracting keywords by stripping unnecessary
characters and formatting. It handles various edge cases such as leading dashes, asterisks, bullet
points, and numbered lists. The function also removes surrounding single or double quotes from
keywords. The final list is truncated to the first 10 keywords.

Args:
    response (str): A multi-line string containing potential keywords, each on a separate line.

Returns:
    List[str]: A list of parsed keywords, limited to the first 10 entries.

The function performs the following steps for each line in the response:
    1. Strips leading and trailing whitespace.
    2. Removes leading dashes, asterisks, or bullet points.
    3. Skips lines that start with numbered lists (e.g., "1.", "2.", etc.).
    4. Strips surrounding single or double quotes.
    5. Adds the keyword to the list if it is non-empty.
"""
You should write code starting with:
from typing import List

def _parse_keywords_fallback(response: str) -> List[str]:
    pass

