If an effect begins to apply to Mirror of the Forebears before it becomes a copy of another permanent, that effect will continue to apply. For example, if Mirror of the Forebears is activated twice in response to itself targeting first Spirit of the Hearth then Temur Sabertooth, the ability it has while it’s a copy of Temur Sabertooth can be activated and its effect will continue to apply while Mirror of the Forebears is a copy of Spirit of the Hearth.