I think that together with Velstadt and Raime they were some elite knights of Vendrick. Kinda like Ornstein, Artorias, Ciaran and Gough were elite knights of Gwyn. While Velstadt and Raime were Vendrick's bodyguards, the Throne Watcher and Defender were to watch and defend the throne.

When the curse hit and Vendrick chose to flee with Velstadt, he ordered the Defender and Watcher to stay back, lock themselves in the cavern with the Throne of Want until a way was found to overcome the curse and/or defeat Nashandra. I picture the plan was for the two of them (Throne Watcher and Defender) to guard the Throne of Want until Vendrick or the new monarch returned to release them from, what was essentially their prison. They were to recognize their savior by the fact that he could unlock the door to the cavern. A failsafe plan, since the only way for someone to open the door was the King's ring and it was heavily guarded by both Vendrick and Velstadt.

But that was very long ango and until we arrive there is no cure for the curse and no one could challenge Nashandra. The plan did not work. When we arrive Vendrick's hollowed remaines walk endless circles in the undead crypt. Velstadt and the royal guard slaughter everyone that dares get near. Their last orders were to not let anyone through to the king, who is now unable to permit entry to their possible savior (i.e. us). During all this time the Throne Watcher and Defender stand guard. It may have been so long that their real names have been forgotten by the outside world.

Now, concerning what Defender and Watcher want or wish for. My best guess is that they want to be free from their duty to protect the throne of want. Since they have been trapped for so long they wish for the curse to be cured, for Nashandra to be defeated and for themselves to be free from their endless guard. But was the wait worth the while? Probably not.

Nashandra probably didn't know about the King's ring that opens the door to the Throne of Want. But she must have tried to open it with pure force when nothing else worked, I imagine. Now I suspect that Nashandra's presence was strong enough for some of the dark to seep though the door into the cavern, slowly corrupting it's occupants. When we arrive Watcher and Defender appear almost hollowed. The long exposure to the dark has made them paranoid. "Surely it couldn't have taken so long to defeat Nashandra. Something outside this door must have gone wrong!" (This could explain their dark souls. Artoria's soul became dark through exposure to Manus, the abyss, himself, Velstadt's soul became dark through exposure to the darkness of the undead crypt, so the souls of the Watcher and Defender may have become dark through exposure to Nashandra.)

But after this long their plan has finally worked out. Even though Vendrick is dead, we are the next monarch coming to take the Throne, defeat Nashandra and cure the curse of the undead. We are everything they longed for.

But even though we seek to cure the curse, we were led by Nashandra up until we open the door to the throne. When we arrive at the throne of want the Throne Watcher and Defender see only an agent of Nashandra, who has managed to break through the door. Their worst fears have come true. And so they attack the next monarch, the person they were defending the Throne for.