A better way to do this exists, I am sure, but I failed to find it easily with Google: How to display a tool tip programmatically in Swing:
ToolTipManager.sharedInstance().mouseMoved( new MouseEvent(targetComponent, 0, 0, 0, 0, 0, // X-Y of the mouse for the tool tip 0, false));
Note the commented line. This is the relative location of the synthetic mouse event to the target component. The (0, 0) example above is as if the user had paused the mouse at the upper-left corner of the component, and the tool tip displays accordingly.
Another choice might be (targetComponent.getWidth(), targetComponent.getHeight()) for the lower-right corner, etc.
I wish Swing had a more straight-forward way of using the tool tip framework programmatically. I would like to be able to reuse tool tips for form validation. But at least this works.
UPDATE: 4 years on and I still get more positive comments on this post than any other. Hopefully the JDK improves in this area.