I wonder if Tolkien was inspired by the story of
The Giant who had no heart - though its a common theme in folklore. The giant is impervious to harm because he has placed his heart in some obect which is hidden away
Quote:
"Far, far away in a lake lies an island; on that island stands a church; in that church is a well; in that well swims a duck; in that duck there is an egg, and in that egg there lies my heart."
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In the same way Sauron's 'heart' is in the Ring. In order to kill him the Ring must be found & destroyed in a certain way.
It has been shown by Shippey that Tolkien often took mythological themes & tried to 'reconstrcuct the 'actual' story that had been lost - see his esay on Light Elves & Dark Elves in Tolkien Studies vol 1 - Norse mythology mentions 'Light Elves & Dark Elves (losalfar & swartalfar), but doesn't explain what they are or what the difference is. Tolkien constructs an 'explanation' & comes up with the Calaquendi & the Moriquendi. Maybe with the relationship between Sauron & the Ring he was doing the same.
Of course, this doesn't offer an explanation in terms of the story of Sauron & its workings within Middle-earth, so we're not much further forward....