Hello, sorry for insisting but I still believe a simple way to achieve it would be a properly tuned monitor + irule redirect.
What I meant was checking specific response string instead of just the 200-OK HTTP code.
Configure monitor to check the specific URI and set as your response string something that is uniquely contained in your expected page, so that monitor fails if it's not found (meaning that logout redirect is seen).
When testing monitor, check it against a working server and then against the "problematic" server while you are in the redirect situation, and check what responses are, then confirm monitor fails when "bad page" is seen.
You can test your monitor like this: (echo -e " <monitor string> ";sleep 1) | openssl s_client -connect <server ip>:<server port>
eg
(echo -e "GET /myapplication/ HTTP/1.1\r\nHost: \r\nConnection: Close\r\n\r\n";sleep 1) | openssl s_client -connect 10.10.10.10:443
Another way to do so would be a two-monitor configuration for the pool, and have the second monitor configured with a receive-disable-string so that if monitor sees logout page content in response it marks the pool member down, which would trigger irule redirect.
Hope this helps
CA