When you open the SystemLogsGUI application, click on Help button and expand section: Using System Log Parser Tool > Using Command Line. Commands can be automated by making a script. If you need more help with System Log Parser, contact Esri Professional Services for consulting.
I am also trying to script the running of the System Log Parser, but my help file contents are largely empty. So although I can see the header you refer to ("Using Command Line") there is nothing in that topic, or in any of the other headers. Do these help docs live anywhere else? If not, can you post a copy here?