WebSockets are a protocol outside of HTTP/HTTPS
They are their own protocol in Tomcat configurations and you use a separate configuration stanza (apart from your normal HTTPS) to configure them
Links:
https://tomcat.apache.org/tomcat-8.0-doc/web-socket-howto.html
https://tomcat.apache.org/tomcat-7.0-doc/web-socket-howto.html
Both of you were very close
Andrei