I am interesting in the ArcGIS System Log Parser. Does it need to be installed on the ArcGIS Server machine or can it be installed on a separate machine and point to the ArcGIS Server URL? If yes, does that machine need permission to access the ArcGIS Server machine? Thanks!
The System Log Parser application will reach out over the network to the Server Admin endpoints for each site it's capturing logs from, so network connectivity to the Admin endpoint (using either the web adaptor or directly via 6443) would be required. That means that the software can run on any machine with the ability to connect to the ArcGIS Server site over port 6443, or 443 if administrative access isn't disabled at the web adaptor level.
You can also run SLP against the file location for the logs. using the ArcGIS Server (FS)