You can use the 13 "Perform Script on Server" to do that. But you have the same script twice: once for the client as a regular script, once as a PSoS call to get it installed on the server.
According to FileMaker's documentation, it is supported as a server scheduled script:
But even if it is, it might just be easier to install it manually, unless you're rolling this out to a bunch of different servers? You could install the plugin in the time it takes you to setup a scheduled script to run.
Your answer made total sense, and I should have thought of it since I use PSoS often. I went astray in my thinking when I tried to find a "Insert Other Symbol" and started looking for "installedHostPlugins" and could not find it.
Anyway after a Duh moment I am back on track!!