Get top (crown) of the head in Python?

Question

How can I get the pixel coordinates of the top of the head for a headshot image in Python?

I've taken a look at dlib with https://github.com/codeniko/shape_predictor_81_face_landmarks as well as the face_recognition module, but neither of them seem to support

Here's the script I've written

# /// script
# dependencies = [
#   "cmake",
#   "pillow",
#   "face_recognition",
#   "dlib",
# ]
# ///

import argparse

from pathlib import Path

import dlib
import face_recognition

from PIL import Image, ImageDraw

def main(image_path):
    image = face_recognition.load_image_file(image_path)
    return features(image)

def features(image):
    # face_recognition
    face_landmarks_list = face_recognition.face_landmarks(image)
    print("I found {} face(s) in this photograph.".format(len(face_landmarks_list)))
    pil_image = Image.fromarray(image)
    d = ImageDraw.Draw(pil_image)
    for face_landmarks in face_landmarks_list:
        for facial_feature in face_landmarks.keys():
            print("The {} in this face has the following points: {}".format(facial_feature, face_landmarks[facial_feature]))
        for facial_feature in face_landmarks.keys():
            d.line(face_landmarks[facial_feature], width=2)
    locations = face_recognition.face_locations(image)
    for top, right, bottom, left in locations:
        d.line([(left, top), (right, top), (right, bottom), (left, bottom), (left, top)], width=2)
    # dlib
    detector = dlib.get_frontal_face_detector()
    predictor = dlib.shape_predictor(str(Path(__file__).parent / 'shape_predictor_81_face_landmarks.dat'))
    faces = detector(image)
    for face in faces:
        x1 = face.left()
        y1 = face.top()
        x2 = face.right()
        y2 = face.bottom()
        landmarks = predictor(image, face)
        for part in landmarks.parts():
            d.circle((part.x, part.y), 2, width=0, fill='white')
    # Show the picture
    pil_image.show()

if __name__ == "__main__":
    parser = argparse.ArgumentParser(description="Process an image to create a proportional passport photo.")
    parser.add_argument("image", help="Path to the image file (jpeg, png, tiff)")
    args = parser.parse_args()
    main(args.image)

and its output:

But the point I am interested in is this one, where the crown of the head would be predicted to be:

How can I get that point in Python?