Dammit. Just 10 minutes after posting this problem, I found the solution. This link was helpful:
Volume, Battery (Power) or Network Icon Disappear or Missing from Vista Taskbar Notification Area (System Tray) » My Digital Life
I had right-clicked on the Notification Area, and selected "Customize Notification Icons...". That allows you to configure the display for everytyhing <except> the four system icons: Clock, Volume, Network, & Power.
However, if you right-click on the Task Bar, select Properties, and then hit the "Notification Area" tab, you can see the checkboxes for the 4 system icons. That's the ticket.
Now I feel stupid, but the issue would not have come up, if SP1 had not changed my settings for those two icons...
Cheers.
JeffS