You don't need to close a PR and open a new one to make changes; you can push new commits to your branch and the PR will be updated.

The test is complicated and looks fragile (for example, it'll break with HTTP/2). I'm pretty sure we don't want to monkey-patch _handle_exception here - if that function is doing something inappropriate, it should be fixed and not patched for this test. It's not clear to me why you're doing what you're doing there.

I think it should be possible to test this with just a custom resolver (a non-blocking resolver that never completes). Does something like this work?

    class TimeoutResolver(Resolver):
        def resolve(self, *args, **kwargs):
            return Future()  # never completes

    client = self.create_client(resolver=TimeoutResolver()))
    self.addCleanup(client.close)
    client.fetch(self.get_url('/hello'), self.stop,
                     connect_timeout=connect_timeout)
    response = self.wait()
    self.assertEqual(response.code, 599)
    self.assertTrue(timeout_min < response.request_time < timeout_max,
                    response.request_time)
    self.assertEqual(str(response.error), "HTTP 599: Timeout while connecting")

All right, I'll make some change.

A non-blocking resolver that never completes works pretty well!😊

Updated, pretty thanks!