Java plug-in no longer in Safari 12.0

After seeing an update for Safari today, I noted that it contained security updates, so I upgraded. After upgrading, however, I could no longer launch a Java applet for remote desktop access that I've used for years. The upgrade put Safari at version 12.0 (13606.2.11). There no longer is a Java plug-in under the list of available plug-ins that can be enabled/disabled for individual web sites. Specifically, it used to look like this:

Now I now longer see Java in the list of plug-ins at the lower left. I re-installed JRE 8 Update 181 from Oracle to no avail. How are we supposed to run Java applets/applications from Safari in version 12.0 and later? My MacOS is Version 10.13.6 (17G65).