A figure in Greco-Roman mythology whose death was mourned by Phoebus/Apollo? That reminds me of Hyacinth:
One day, Apollo was teaching him the game of quoit. They decided to have a friendly competition by taking turns to throw the discus. Apollo threw first, with such a strength that the discus slit the clouds in the sky. Hyacinth ran behind it to catch it and impress Apollo, but as the discus hit the ground, it bounced back, hitting Hyacinth's head and wounding him fatally. Alternatively, Zephyrus is held responsible for the death of Hyacinth; jealous that Hyacinth preferred the radiant Apollo, Zephyrus blew Apollo's quoit boisterously off course to kill Hyacinth.
Apollo's face turned pale as he held his dying lover in his arms. He used all his medicinal skills and even tried giving ambrosia to heal Hyacinth's wound, but in vain, for he could not cure the wound inflicted by the Fates. When Hyacinth died, Apollo wept, blaming himself. He wished to become a mortal and join his lover in death. However, as that was not possible, Apollo promised that he would always remember Hyacinth in his songs and the music of his lyre. From Hyacinth's spilled blood, he created a flower, the hyacinth, and on its petals inscribed the words of despair, "AI AI" – "alas".
A gem bearing the name of Hyacinth? There you go:
Jacinth or hyacinth is a yellow-red to red-brown variety of zircon used as a gemstone.
So the passage you've quoted is a roundabout way of referring, among many other gemstones listed in the same stanza, to jacinth.