360works has remote scripter that will allow you to execute remote scripts on other FM machines.
It's listed as supporting server version of FM.
There's a couple other plugins that do this as well. We've used it before to send commands to "drone" computers, but our need has waned over the years.
Best practice is still to configure FM server with a static backup schedule (FM12 brought great new options for incremental backups as well), this way your IT department (or you) can verify on a tight schedule of when a backup was run.
You can also make a "one time backup" schedule that you access through the server control panel remotely (serverip:16000), and execute anytime that you need it.