how can i troubleshoot an irules logic

I would just add that a good rule of thumb, whenever accepting input from the client, is to normalize that input before trying to evaluate it. For string values, I'd use the [string tolower ] function and make sure the values in your data group are also lower case.

when HTTP_REQUEST {
    if { [class match [string tolower [HTTP::host]] contains PROXY_VM] } { 
        pool PROXY_VM
    } elseif { [class match [string tolower [HTTP::host]] contains GSI_LIST] } {
        pool GSI_PROXY 
    } elseif { [class match [IP::client_addr] equals INTERNAL_IPLIST] } {
        pool PROXY_VM 
    } else {
        pool PROXY_POOL
    }
}