Pelinal is a version of Shezar, who gave Alessia the amulet on her deathbed. The story talks of Shezar/Akatosh ripping out his heart (the exact place the amulet was in Pelinal) and giving to Alessia. Its also a symbol of how vital Pelinal was to the rebellion and how vital the rebellion was to Pelinal.
What to have your mind blown? The Amulet of Kings (that is Chim-et-Adabal) was made by the Ayleids as the stone to the White Gold tower
Indeed, the Amulet is a very important piece of lore. It's tied in with the Towers, the relationship between Lorkhan and Akatosh, the Alessian Rebellion, the Covenant, etc.
The Song makes it a little fuzzy (at least to me) of when exactly Alessia gets the Amulet. My favorite idea is that Pelinal has the Amulet, the answer to her prayers, from the get go, and as an avatar he is that Stone's Guardian. So if it is the Stone to begin with, then did Pelinal take it from some Ayleids? Or did Akatosh/Lorkhan take it from them and give it to their avatar?
Really gives new meaning to the star shaped hole in his chest
PS Real quick, was the Liminal Barrier up before Alessia's death? Since that was when they made the Covenant with Lorkhan (Shezzar)/Akatosh, and is apparently what Martin changed at the end of Oblivion. Just wondering