private final int defaultDismissTimeout = ToolTipManager.sharedInstance().getDismissDelay();

addMouseListener(new MouseAdapter() {

  public void mouseEntered(MouseEvent me) {
    ToolTipManager.sharedInstance().setDismissDelay(60000);
  }

  public void mouseExited(MouseEvent me) {
    ToolTipManager.sharedInstance().setDismissDelay(defaultDismissTimeout);
  }
});

private PopupFactory popupFactory = PopupFactory.getSharedInstance();
private Popup popup;
private JToolTip toolTip = jEditorPane.createToolTip();

private void showToolTip(MouseEvent e) {
    toolTip.setTipText(...);
    int x = e.getXOnScreen();
    int y = e.getYOnScreen();
    popup = popupFactory.getPopup(jEditorPane, toolTip, x, y);
    popup.show();
}

private void hideToolTip() {
    if (popup != null)
        popup.hide();
}