Thanks @Nige_S,
I'm running Mojave still, so maybe that's the difference. In Script Editor, there is no Save As option, only Export. When I choose Export, then there are File Format options. If I pick Application, then I can optionally choose "Stay open after run handler".
WHICH BEGS another question, aimed at EVERYONE:
When I run the Stay Open app, how do I quit it?
Update: Rebooting worked. The problem has not recurred.
It doesn't show up in the Activity Monitor or in the Force Quit menu. Everything that I've found by Googling says to simply Quit the app, sometimes they say to use its Quit button, one example even implying that the Quit button will be available automatically somehow. But there's no button, no window for this app while it's running in Stay Open mode.
How do I quit the Stay Open AppleScript app?
I tried starting it a second time. This time CJKsNotifyOnSpaceChange
shows up in Activity Monitor. When I select it there and click the Info button, I see some process information and a Quit button. I can quit that instance. But the original one that I started this morning is still running and I can't find it to quit it.
I created a new script/app with a new name, this one adding the operation to call a KBM macro. When I export that as an app I also got the option to show a start menu. I did that and got Run and Quit buttons, but that dialog goes away when I press Run, so there's still no Quit button. That app name shows up in both Activity Monitor and in the Force Quit menu, so I can quit it.
And the hidden version continues to notify me of Space Changes, and I can quit it.
I really don't like rebooting having to be part of my script debugging cycle, but maybe that's it. But how did I get there?
Could I have created this "ghost process" by changing the name of the file while it was running?