I believe the Head is Tireces.
The Leveler is a spirit that comes down and takes over the body of the hero that last defeated him. He only leaves when he is once again defeated.
I seems the only way to kill the Leveler is to cut off his head. All three of the ones they mentioned had this happen to them. Drawing & quartering involves removing the head, and why would they put emphesis on "His BODY was destroyed by fire" and not just say "he was destroyed by fire," if his head wasnt cut off?
Once the head is cut off, the armies of the Dark collapse... but remember, the Head of Balor was still talking to you after it was cut off... perhaps the Leveler instills so much power in his host that the former Hero is still in that head somewhere after the Leveler flees... But insane, deranged, mad. The Head could be the great hero Tireces, who was taken by the Leveler and forced to watch helpless through foreign eyes as Moagim, through his body, raised the Myrkridia and brought unspeakable horrors on the world... Who wouldnt go insane, when, after three hundred years of this, the Leveler finally flees what is left of your being? And if he wasnt mad then, a thousand years buried under the desert would have turned from from a noble hero to an insane bringer of chaos.