This problem has been solved thanks to help from Universal Devices Forum members, and I finally found the correct pages at Java.com.
I needed to obtain the newest "start" program from Universal Devices, which is supposed to create a new Launcher icon. Which it does, only if you clear your Java cache first, but the launcher icon doesn't work on macOS 10.13 it requires 10.15. But I can start my ISY console by running the start program every time anyway...no big deal.
I found the Q/A page at Java.com which explains that if the Update dialog in the Java Preferences fails to work, you can simply install the latest version. It is not necessary to remove the old version first. Then I found the download page which identifies your OS and allows you to download the latest version by pressing the DOWNLOAD button.
https://www.java.com/en/download/
It wasn't that hard, though I had to wait a few days to get replies and have time to figure everything out.
I still think Java makes life more difficult. I have programs going back 20 years which still run fine, and I never had to do any special update of anything.
Sadly when I move on past macOS 10.13.16 all the old stuff will be unuseable. That's the thing I hate the most about OS and computer upgrades. I will need to retain my current computer, or some replacement, running 10.13.16 just to keep the old programs going, and buy a whole new computer in a few years with the latest everything. When I have time and desire to deal with it.
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On Mac, I had been using the ISY994i Admin Console for years, including a few months ago. The one I have is dated August 27, 2015. The ISY994 Dashboard is dated November 25, 2017. I cannot update the console via the webpage sometimes discussed because that fails too in a similar way (described further below).
Both the console and the dashboard fail with "Unable to Launch Application." It doesn't help to use "Open" to open the application. The Details page shows "illegal URL redirect" at top of traceback list.
The Java Preferences do not seem to be useful. The "About" says I have version 8 Update 331 (1.8.0_331-b09) which is from this year (but current???). When I go to the Java Update tab, I see a rotating circle that just rotates forever. Reading about Java on the Java website (never a pleasant experience) it appears that this is the only way to "Update Java. " And it is "stuck" apparently, either that or I do have the latest version, I can't tell.
I went to the page to re-download the ISY Administrative Console. I click on the link https://isy.universal-devices.com/start.jnlp and it downloads. I click on the file and it says "start.jnlp cannot be opened because it is from an unidentified developer". I tried both clearing the cache and adding https://forum.universal-devices.com to the Java Exception site list and neither helped.
UPDATE:
Problem was fixed by going to System Preferences, opening up the Security & Privacy page, selecting the General tab, clicking on the lock to open it, entering my password, and THEN running the new "start.jnlp" downloaded from Universal Devices. Note that I already did have the Allow App Store & Identified Developers box checked, and there is no other box. But just opening the lock let me run the app once, and after that I can keep running it even when the lock is closed (which happens automatically if I leave the Java Preferences).
So the trick is you can run apps from unidentified developers but only if you click the lock on this page. I suppose that's not too bad (though I still think it's Securanoia) but why doesn't Apple have any explanation on this page or anywhere else.
You either know the secret handshake or you don't, it appears. I've been here before I think, but it was about 5 years ago last time, so I forgot.
Seeing how well computer systems without "AI" work, it's easy to imagine that when we do have computer systems with "AI", they'll be even more frustrating, and we'll pull the plug and just go back to using hand tools.
I still don't know how to update my Java since the Java Preferences itself is unable to do that. I see now that it clearly has expired just a few days ago (it says that in some Java tracebacks). There was a time you could just go to the Java website and it would identify your system and Java version and tell you what to do. But they took all that out, apparently, probably because others were spoofing it. Now you can only update through the update app. The Java website does not make it clear how to do anything else.