In Skyrim, items are labeled "Persistent" when they need to be, like when a REF is set as an ObjectReference Property. You don't have to manually ensure stuff is persistent as it will happen automatically.
The game itself decides if a Ref needs to be persistent or not. Examples of things that make a ref persistent:
* Forced Fill Alias pointing at it
* Script property pointing at it
* Being an enable parent for other refs
This isn't an exhaustive list, but you get the idea. For actors, the "Persist Location" is an additional factor that determines when the actor starts persisting - the general idea is to only have actors persist (e.g. running their AI) when they need to be. So for example, all the NPCs in any city use that city's Location as their Persist Location, so that they can run AI when the player enters the city location, but otherwise not.
Not sure about ungluing items though. Try ~Player.RemoveAllItems XXXXXXXX being the FormID of a container REF, then take it all back and Strange Amulet(s) should be unglued.