I have asked about the missing system tray over on Ubuntu Forums, but nobody seems interested in the question. It is frustrating because a few programs minimize to the system tray instead of shutting down, and so I don't have an easy way to access them. Anyway the system tray appears and disappears seemingly at random during a session. System reboot doesn't help. I tried the suggested actions in this answer with no luck. So, I'm stuck. Really could use some help with this.
Edit 1: Just to get a baseline, I rebooted and printed out the currently running programs here using the following command:
top -n 1
If there is any more system state information that would be helpful, I will get it up here as I learn about it.