You cannot use the effect to burn the card and the vampire if the vampire is no longer in play to be burned.
100665
The Eternal Mask
+1 stealth action.
Ⓓ Bleed with +1 bleed.
Put this card on this vampire and move a unique vampire from any ash heap to your ready region with any amount of blood from this acting vampire. The attached minion cannot perform actions, block, play reaction cards or cast votes or ballots. You can burn this card and the chosen vampire during any unlock phase.
Rulings
You still cannot burn it if the vampire that was brought back was burned and later returned to play.
If The Eternal Mask is burned by something else than its own effect (including when the vampire it is on is burned), the vampire that has been brought back is unaffected.
Is an undirected action, even when targeting another Methuselah's ash heap.
Cannot be played if no target is available in any Methuselah's ash heap.