Identifying specific Header and logging time they attach?

The rule could be as short as:

        
     when HTTP_REQUEST {     
     if { [HTTP::header exists "True-Client-IP"] } {     
             set LogString "[IP::client_addr]"          
             log local0. "$LogString"          
          }          
     }     
        

The date and timestamp would be added by your logging facility, yielding lines that should look something like this:

        
        Dec 10 11:43:09 bigip tmm tmm[1653]: Rule simple_timestamp : 10.10.10.102        
        

(the odd character is the forum trying to render the PID as a control character of some kind)