You can have multiple versions of the quest open at the same time.
There is no "Unlocking a Myth" quest for Rune Fencer or Geomancer, the two jobs which do not have Nyzul Weapons. The Geomancer equivalent quest is Geomancerrific, and the Rune Fencer equivalent is Rune Fencing the Night Away.
Weapon Skill Point Requirements
- Regardless of Nyzul Isle Investigation progress, only 250 Weapon Skill Points are needed to complete any Unlocking a Myth quest as of July 2014.