Thanks to everyone who has written back to me. These articles and suggestions were very informative.
I have solved the problem on one of the computers running EndeavourOS, the one I use for experimentation.
If anyone is interested, here is what I did.
I installed OpenNTPD, removing NTP. I rebooted and nothing (the time showing on my computer) changed. The time was still wrong.
I looked for any OpenNTPD program I could adjust and, finding none, I went into systemd-manager, scrolled down, and there it was. It was not active.
In the terminal, I typed sudo systemctl enable --now openntpd and that activated it (both indicators were green).
But, after rebooting, again nothing had changed.
I went back into systemd-manager and looked more closely at the parameters of openntpd and I saw that there was a message stating that this program was in conflict with systemd-timesyncd.service.
So I typed sudo systemctl enable --now systemd-timesyncd.service and, after rebooting, the time was now set correctly. Hooray!
But I didn’t stop here. I went back into systemd-manager and, scrolling down, I saw that only the left indicator of OpenNTPD was green; the right indicator was red (off).
And the conflict message was still present.
At that point (and remember, the time showing was now correct), I decided to remove OpenNTPD and replace the original NTP program.
I did so and, after rebooting (again!), I went back into systemd-manager and scrolled down to ntp. I saw that both indicators were red (off) and there was the same message that ntp was in conflict with sudo systemctl enable --now systemd-timesyncd.service.
The time was still set correctly - and there is remains (at least so far).
So there I stood. I decided that that was it. I have left ntp “off” (both indicators red) and systemd-timesyncd active (both indicators green). The time is now apparently synchronized with NIST.
I’ll see what happens with this computer over the next few days and, if the time stays synchronized, I’ll effect this sudo systemctl enable --now systemd-timesyncd.service on all of my EndeavourOS computers.
It appears that this one command is the only thing you need to enter in order to ensure that your computer’s time is set to the standard time set by your local time service.
Thanks again to all for pointing me in the right direction.