How can I trigger a CLIENT_DATA event manually?

The purpose of 'TCP::notify response' is to raise the USER_RESPONSE on the client side so that you can detach the serverside connection after all the data has been delivered to the client. You only need to call it once when you have received all the response data.

when SERVER_DATA {
   log local0.debug "Received SERVER response ... [TCP::payload]"
   if { [TCP::payload] ends_with $EOT } {
      TCP::notify response
   }
   TCP::release
   TCP::collect
}
when USER_RESPONSE {
   LB::detach
   log local0.debug "Detaches server connection ... "
   if {[TCP::payload length] > 0} {
      
       %TODO%
       Process additional client requests here ...
      
   }
}

Is your response length delimited? If so, I would suggest that you change your response logic to use length counter rather than look for the magic EOT string. The longer your magic sting the greater the chances of it being segmented into multiple packets.