9135: Make EventClient initialization more consistent.

9135: Make EventClient initialization more consistent.

* DRY up the setup code.
* Make the client a daemon thread, for consistency with PollClient.
* Always try to close the connection on failure.  We do this in
  _subscribe_websocket, so why not do it on reconnect as well?
* Remove the public connect() and close_connection() methods from
  EventClient.  They're no longer needed, and avoid leaking
  implementation details.