I did a power off reboot and it works that way. ITAC was very co-operative and helpful, quickly shipping a second trackball for me to try. It looks like I first tried rebooting, I just went down to single user mode and then rebooted without powering off, and that doesn't work.
This seems counter-intuitive since USB is supposed to be hot-swappable. Going from a mouse to a trackball and vice versa isn't hot-swappable, but apparently once the proper driver is in place, you can replace a device in kind without a reboot.