While my laptop gave the task tray icon to reserve my copy, the Windows 8.1 partition on my desktop did not, even with all the Windows updates installed.
I think the problem I had with my desktop is that I had roughly 10GB of free space on the OS partition as I stored VirtualBox images on it.
I freed up about 30GB by moving old images to a hard disk and ran this script Microsoft posted. The script ran for about 10 minutes and the icon appeared once the script completed.
So for anyone else who doesn’t see this icon, check if the OS partition (‘C’ drive) has plenty of free space.