Please do. The goal of catching the PD-S-SESSION-ID-PROD2 cookie was based on the assumption that it was being set in the 401 from the PoolK member.
if { [HTTP::status] == 401 and [HTTP::cookie exists "PD-S-SESSION-ID-PROD2"]} {
A cookie would only exist in a response message if it was a Set-Cookie. Given that, I think you now need something other than the presence of this cookie in the request to indicate that auth is happening or has happened. Is there something else that the poolK server sets or sends to indicate that auth is happening/successful?