OK I saw this icon on a Windows 7 computer today. It's the icon for the "Interactive Services Detection", which is part of Windows since Vista.
It's caused by Services and/or Processes running under the System or another account in the background, which are requesting Desktop Access.
Since Vista and above separate this from the user session, this Icon would (if you could click on it fast enough) lead to a pop-up, that would allow you to see the message(s) the background process is trying to display, and find out what's displaying it.
More info here: What is Interactive Services Detection and Why is it Blinking at Me?
This page: Troubleshooting Interactive Services Detection explains some troubleshooting tips on how to deal with it.
It has a specific section entitled "The Tile Button is Displayed Too Quickly and I Can't Click it Fast Enough", which sounds like what you're running into.
It has instruction on how to use the Windows Event Viewer to capture the Interactive Services Detection process and log it, that way you can check out the Event Logs to see what's triggering it.
Here's the instructions they provide:
- From the Start menu search box, type
eventvwr to start the Event Viewer.
- In the tree view in the left pane, right click Custom Views and select Create Custom View...
- In the Custom View dialog, select the "By Source" radio button and then select Interactive Services Detection in the "Event sources" drop down box.
- Click OK.
- In the "Save Filter" dialog, name your custom view. e.g. "Interactive Services Detection".
- Click OK. You are now configured to capture these events when the occur.
Then, the next time you see the Interactive Services Detection icon appears on the taskbar, you can return to the Event Viewer and investigate the information that has been logged.
Example ("Calculator" was what tried to pop up the message):