Second Relic Weapon

[Venat]

I'm currently leveling my second class to 50. I've already done my Relic Reborn Quest on my Summoner, and have heard that we can obtain the relic weapon on every class/job. Upon reaching level 50, will the relic reborn quest just... re-appear in vesper bay if I have my newly level 50 class/job equipped?

gotta get it to 50 and do all class/job quests before you can select that relic for that job.