He should just say whoever Cirie wants to save can use the HII to save herself if she wants while he keeps the necklace. He may not try for immunity because he likes the idea of a blindside using the HII like Amanda did but I doubt it. He could use the same excuse, let the other person use the HII. How do they they explain to the others why he gave his necklace away?

The closest I can think of is if Eric only tries for immunity if a certain person is leading. If the person they want to save is close then Eric lets them win because he has the HII as backup. The others would all have to play along and let the person win. That way it is not as obvious as just giving the necklace away and leaving himself unprotected.