5th dnd – Can a spectator be a bodyguard? So, can his treasure / object to keep be an object / a person?

In 5th, the rules do what they say (and all that remains to be done belongs to the DM to decide). The attention of the viewer is focused on "a place or a treasure". His mandate is "to allow no other creature than his summoner to enter the area or access the object …"

A living being is neither a place, nor a treasure, nor a place nor an object.

Even if it was the case, it would not have the desired effect. It does not keep the body, it prevents access. Even if it could be attributed to a person, he would not be able to distinguish between stabbing with a knife and shaking his hand. A bodyguard who can not tell the difference between these two things is not a particularly effective bodyguard.

As far as the necklace, it could job. It's a legitimate treasure, no one has stolen it, and nothing says that a spectator must stay in one place.
This would certainly help prevent anyone from stealing the collar or removing it from your body as it cools down. On the other hand, this will do very little on the part where they convert you to a cooling body in the first place. What does it matter to the viewer if someone pulls you holes? You are not the one that he keeps.

… and if you persuade the viewer that anyone within 20 feet of the necklace is a threat? Well, have fun walking down a street.

This is not the use of this tool, it is not suitable for the intended purpose and it will not work.

Well, a spectator is summoned and bound by a specific ritual that does a specific thing. It would be perfectly reasonable to assume the existence of a similar but distinct ritual, which would have had the same task of summoning a spectator (or something that would look much like a spectator) as a guard of the body. If it's something you want to have in your game, it's a quite reasonable thing to have in your game.