Currently, the WebSocket client fails to connect if it receives a 302 redirect. It would be a useful enhancement to follow the redirect.
That's included in 57767 (for trunk). I looked a bit at Tyrus, and it is a fairly standard HTTP client (with a lot of proprietary config for all its features), while the websockets client in Tomcat can't do anything besides upgrade. OTOH, a webapp that needs a websocket client does not need to use the Tomcat one, so a valid strategy could be to do nothing. Which is nice since ultimately the only real solution is to use HTTP client or something big like that ...
*** This bug has been marked as a duplicate of bug 57767 ***