Rabbotai,
R. Elazar B'R. Tzadok said that he came from Shebet Binyamin's Snaav family
and they had a personal Yom Tov on the 10th of Av because they would bring a
"Korban aytzim" - wood for the maaracha on that day. They didn't finish the
fast on Sunday, the 10th of Av for this reason.
1) Did people mourn the 1st Bais Hamikdash's destruction while the the 2nd
Bais Hamikdash stood? What would they daven for - that it should be rebuilt? It had been rebuilt.
2) Did R. Elazar B'Rav Tzadok actually live during the 2nd bais Hamikdash? If he lived during Rabban Gamliel's time it would be after the churban as the churban happened during the time of Rabban Yochanan Ben Zakkai seemingly a few generations earlier.
3) If indeed he lived after the churban would his family still celebrate the
day that they used to bring the wood (10 B'Av) after the churban?
B'kavod,
Sam Kosofsky
Excellent points! If Rebbi Elazar b'Rebbi Tzadok lived during the time of the Beis ha'Mikdash, why was the rest of the nation fasting on Tisha b'Av, and if he did not live during the time of the Beis ha'Mikdash, why did he have a Yom Tov on the day of his "Korban Etzim?" (Indeed, Rebbi Elazar b'Rebbi Tzadok lived both before and after the Churban, as we find that his father, Rebbi Tzadok, was one of the elders of Israel at the time of the Churban. See Gitin 57b.)
a) TOSFOS (Ta'anis 12a, DH Hasam) mentions that the incident of Rebbi Elazar b'Rebbi Tzadok occurred after the Churban, since he fasted on the Ninth of Av (see also Tashbatz 2:271, who says that they did not fast on Tisha b'Av during the time of the second Beis ha'Mikdash). Ha'Rav Moshe Sternbuch, shlit'a, proves from here that even after the Churban, they observed their families' Yom Tov, in commemoration of the day on which their families used to bring the Korban Eitzim during the times of the Beis ha'Mikdash (see Mo'adim u'Zemanim 7:212).
b) It is worth noting that the RAMBAM (Perush ha'Mishnayos, Rosh Hashanah 1:3) has a novel approach to this topic. He maintains that even during the time of the second Beis ha'Mikdash, they fasted on Tisha b'Av (that is, close to the time of the Churban, when the Jews no longer had dominion in their land). According to the Rambam, it makes sense to say that the incident of Rebbi Elazar b'Rebbi Tzadok occurred during the time of the Beis ha'Mikdash.
Be well,
-Mordecai