I'm researching the biblical references to the "House of Nathan" in Zechariah 12:12 in context of mourning rituals in post-exilic Judah. What extra-biblical sources discuss the identity and potential duties/roles this clan descended from the prophet Nathan may have had?
Specifically, is there any evidence in sources like the Dead Sea Scrolls, Josephus, rabbinic writings, etc. that sheds light on:
How this clan traced its lineage back to Nathan son of David
If they held a recognized position overseeing aspects of mourning/lamentation rituals
Any specialized priestly or musical/literary responsibilities within temple or community worship
Comparisons to other prominent priestly families like Levites, how their influence/duties were defined
Any other details about their identity or place within the religious leadership of Judea after the exile
Any information or directions to relevant sources that could help elucidate this minor but important biblical reference would be greatly appreciated.