Happy Eyeballs solution using gevent modeled after Nathaniel J. Smith's canonical version for Trio

happyeyeballs.py

import gevent
import gevent.event
import gevent.socket
import gevent.pool

def open_tcp_socket(hostname, port, *, timeout=0.250):
    targets = gevent.socket.getaddrinfo(hostname, port, type=gevent.socket.SOCK_STREAM)
    result = gevent.event.AsyncResult()
    group = gevent.pool.Group()

    def attempt(target):
        *socket_config, _, socket_target = target
        socket = gevent.socket.socket(*socket_config)
        socket.connect(socket_target)
        result.set(socket)
        group.kill()

    for target in targets:
        group.spawn(attempt, target)
        result.wait(timeout=timeout)
        if result.ready():
            break

    try:
        return result.get()
    except:
        raise OSError("failed")

print(open_tcp_socket("debian.org", "https"))