It might be easier just to make it a TextBox, set the BorderStyle to None, set the BackColor to Control and set ReadOnly to True.  This should give the appearance of a label, but still allow it to be tabbed onto for focus.
Update It looks like with a combination of SetStyle(ControlStyles.Selectable, true); and TabStop = true;, you can get the Label to focus using the Tab key.  Below is a simple example that shows it working:
public class SelectableLabel : Label
{
   public SelectableLabel()
   {
      SetStyle(ControlStyles.Selectable, true);
      TabStop = true;
   }
   protected override void OnEnter(EventArgs e)
   {
      BackColor = Color.Red;
      base.OnEnter(e);
   }
   protected override void OnLeave(EventArgs e)
   {
      BackColor = SystemColors.Control;
      base.OnLeave(e);
   }
   protected override void OnMouseDown(MouseEventArgs e)
   {
      this.Focus();
      base.OnMouseDown(e);
   }
}