HTTP redirection issue

There's generally two ways to handle this, both depending on how the information is presented to the client.

For HTTP 30x redirects, the Redirect Rewrite setting in the HTTP profile will automatically rewrite http:// to https:// in outgoing redirect Location headers.

For everything else, you'd need an iRule and a STREAM profile. Insert an empty STREAM profile into the VIP's configuration and an iRule like this:

when HTTP_REQUEST {
    HTTP::header remove Accept-Encoding
    STREAM::disable
}
when HTTP_RESPONSE {
    if { [HTTP::header Content-Type] contains "text" } {
        STREAM::expression {@http://@https://@}
        STREAM::enable
    }
}

This works by enabling the STREAM profile on egress text-based traffic only to replace any instance of "http://" with "https://" in the response payload.