> I'm happy to produce a patch if there's any chance it would be merged.

If the patch adheres to the RFC, then I see no reason why it shouldn't be merged. What makes this a little more tricky than the snippet that you included in your post though (which would include the Content-Length header for all HTTP methods) is the following from RFC 7230:

   A user agent SHOULD send a Content-Length in a request message when
   no Transfer-Encoding is sent and the request method defines a meaning
   for an enclosed payload body.  For example, a Content-Length header
   field is normally sent in a POST request even when the value is 0
   (indicating an empty payload body).  A user agent SHOULD NOT send a
   Content-Length header field when the request message does not contain
   a payload body and the method semantics do not anticipate such a
   body.

Currently, there is nothing in the http package that defines whether or not a given HTTP method expects a body (as far as I'm aware at any rate), although this would be a simple addition. I'd imagine that the result might look like this:

_METHODS_EXPECTING_BODIES = {'OPTIONS', 'POST', 'PUT', 'PATCH'}

if method.upper() in _METHODS_EXPECTING_BODIES and \
        'content-length' not in header_names:
    self._set_content_length(body)

I'd prefer to have the conversion from None to empty string done in the body of _set_content_length in order to ensure consistency should the call be made from elsewhere.