requests treats urllib3's SSL handshake timeout as ReadTimeout

Expected Result

When connecting to a remote machine via SSL/TLS, and SSL handshake timeout happens, I expect to have SSLError or ConnectionError exception.

Actual Result

requests raises ReadTimeout

Reproduction Steps

I don't know how to reproduce this, but I have a real stacktrace (most recent call first):

timeout: _ssl.c:704: The handshake operation timed out
  File "urllib3/connectionpool.py", line 346, in _make_request
    self._validate_conn(conn)
  File "urllib3/connectionpool.py", line 850, in _validate_conn
    conn.connect()
  File "urllib3/connection.py", line 326, in connect
    ssl_context=context)
  File "urllib3/util/ssl_.py", line 329, in ssl_wrap_socket
    return context.wrap_socket(sock, server_hostname=server_hostname)
  File "python3.5/ssl.py", line 385, in wrap_socket
    _context=self)
  File "python3.5/ssl.py", line 760, in __init__
    self.do_handshake()
  File "python3.5/ssl.py", line 996, in do_handshake
    self._sslobj.do_handshake()
  File "python3.5/ssl.py", line 641, in do_handshake
    self._sslobj.do_handshake()
ReadTimeoutError: HTTPSConnectionPool(host='somehost.com', port=443): Read timed out. (read timeout=5)
  File "requests/adapters.py", line 440, in send
    timeout=timeout
  File "urllib3/connectionpool.py", line 639, in urlopen
    _stacktrace=sys.exc_info()[2])
  File "urllib3/util/retry.py", line 357, in increment
    raise six.reraise(type(error), error, _stacktrace)
  File "urllib3/packages/six.py", line 686, in reraise
    raise value
  File "urllib3/connectionpool.py", line 601, in urlopen
    chunked=chunked)
  File "urllib3/connectionpool.py", line 349, in _make_request
    self._raise_timeout(err=e, url=url, timeout_value=conn.timeout)
  File "urllib3/connectionpool.py", line 309, in _raise_timeout
    raise ReadTimeoutError(self, url, "Read timed out. (read timeout=%s)" % timeout_value)
ReadTimeout: HTTPSConnectionPool(host='somehost.com', port=443): Read timed out. (read timeout=5)
  File "wsa/external/soap.py", line 234, in call
    response = command(**params)
  File "zeep/client.py", line 45, in __call__
    self._op_name, args, kwargs)
  File "zeep/wsdl/bindings/soap.py", line 113, in send
    options['address'], envelope, http_headers)
  File "zeep/transports.py", line 95, in post_xml
    return self.post(address, message, headers)
  File "wsa/external/soap.py", line 75, in post
    return super(NonPersistentTransport, self).post(address, message, headers)
  File "zeep/transports.py", line 67, in post
    timeout=self.operation_timeout)
  File "requests/sessions.py", line 555, in post
    return self.request('POST', url, data=data, json=json, **kwargs)
  File "requests/sessions.py", line 508, in request
    resp = self.send(prep, **send_kwargs)
  File "raven/breadcrumbs.py", line 297, in send
    resp = real_send(self, request, *args, **kwargs)
  File "requests/sessions.py", line 618, in send
    r = adapter.send(request, **kwargs)
  File "requests/adapters.py", line 521, in send
    raise ReadTimeout(e, request=request)

System Information

$ python -m requests.help

{
  "chardet": {
    "version": "3.0.4"
  },
  "cryptography": {
    "version": ""
  },
  "idna": {
    "version": "2.6"
  },
  "implementation": {
    "name": "CPython",
    "version": "3.5.3"
  },
  "platform": {
    "release": "3.10.0-693.5.2.el7.x86_64",
    "system": "Linux"
  },
  "pyOpenSSL": {
    "openssl_version": "",
    "version": null
  },
  "requests": {
    "version": "2.18.4"
  },
  "system_ssl": {
    "version": "1000105f"
  },
  "urllib3": {
    "version": "1.22"
  },
  "using_pyopenssl": false
}

$ openssl version

OpenSSL 1.0.2k-fips  26 Jan 2017

$ cat /etc/redhat-release
$ uname -spori

OS: CentOS Linux release 7.4.1708 (Core), Linux 3.10.0-693.5.2.el7.x86_64 x86_64 x86_64 GNU/Linux

Start in requests/adapters.py at the exception handling and trace back through urllib3/connectionpool.py's _raise_timeout using the supplied stacktrace. Check how SSL handshake timeouts are classified, then add regression coverage for the reported exception type and verify the existing test suite.