Gaudric is the key, without speaking to him " A tempest Spirit " will not spawn. Also after just finishing this quest , my advice is to get the Amulet first, then speak with Gaudric , to spawn "A Tempest Spirit".
Very easy quest, but as always , read carefully or you may miss a step.
I went to the LoC you provided and did not find him. When you gave him the Amulet did he De-Spawn. If he didnt then he is not here now. If he does , whats the timer on this mob. That would be some great info to have here.