Ziraili did not leave Eldrian without an answer. Just after he asked for a weapon, she delivered. Right in the middle of the room.
It was a normal spear, without any gems or fancy additions. It likely was made of something other than normal iron and wood, else it would be useless against Eldrian's foe. But it was a spear of wood and metal. Kinds are unknown.
And it was right there, for the taking. Only... there was one big something in the way. Granted, the basilisk wasn't directly in Eldrian's path. But if you drew a line from it to Eldrian, to the spear. It would make a rather narrow triangle.
Facing the basilisk head-on had been tough, especially with Ziraili allowing it to use magic and preventing all his standard crutches. Eldrian just knew that letting the basilisk attack from the side or back would spell his end.
