Thank you for your response, Randy-12.
I had tried that with no joy, alas. On the watch, my name doesn't appear under settings, so I'm not sure the information is still current.
I went back to the idea that perhaps I wasn't signed into my Apple ID on the watch. I couldn't see anywhere to do this on the watch, so I used the watch app on the phone. When I viewed the Apple ID, the password field was empty and the Sign In link appeared. I signed in, and then went to the watch Find Devices setting. Sure enough, my phone showed up and was able to send a notification sound to the phone.
I'm not sure how the Apple ID connection became dropped since the time I paired the two. It worked fine at first. This leads me to believe I may need to use Find Devices from time to time and to sign in from the phone's watch app when needed to ensure they stay connected.
Looking back at the Apple ID settings on the phone after this, the password field is empty again and the Sign In link appears, but it looks like my watch has remained connected (Find Devices still shows the phone and I'm able to send an audible alert to it). I also see that Notify When Left Behind is enabled.
So thanks again. I hope your and my posts here help someone else.
Cheers.