Okay, wait, I think I might have it now.
It seems that Windows 7 has some touchscreen/tablet stuff integrated with it for use with some of their newer products that utilize that sort of thing. Naturally, it doesn't play nicely with Wacom tablets, or any third-party tablet, from what it seems like.
I found two threads discussing it on another forum. I'll put up the links at the bottom, but this seemed to be the most promising solution:
"This was posted on another website, worked for me!
Open command, then type in gpedit for the first instruction.
I have found the solution:
Open Local Group Policy Editor. It is quite hidden - search for it in Windows Start menu or in Control panel - use the search box as I have not found the shortcut for it. Alternatively you can run gpedit from command line (not from Run in Start menu).
Navigate to User Configuration - Administrative Templates - Windows Components - Tablet PC - Cursor.
Enable the Turn off pen feedback setting."
If it doesn't work though, it seems like there might be a few other workarounds people figured out too.
First thread for all of that: http://www.sevenforums.com/hardware-devices/18167-wacom-tablet-blinking-cursor-problem-2.html
Second Thread: http://www.sevenforums.com/hardware-devices/11375-wacom-tablet-ring-round-pen-cursor.html