I voted for "toolbar"

Toolbar is a category of application that snaps into the taskbar. I suggested that this would be a good way to handle Fitaly - away from applications - and here I'm doing so again ;-) A catch is that the taskbar is at the edge of the screen and your digitiser may not allow accurate pen work there.

However, I have a script for the AutoHotkey tool that is maintaining my Fitaly in a taskbar location - it's pasted over the TIP button, about 8mm from screen edge. The script has to stop the taskbar either pushing Fitaly back into application/desktop space, or painting on top of Fitaly, and it does this by reminding Fitaly regularly (every 2 seconds) to be on top and at a particular location. I think I shared that one here...

The TIP doesn't seem open to third-party enhancement - its methods are secret - but here also you'll find another clever lad's script that notices when the TIP popup button appears, and pulls up Fitaly to that location instead.