When exactly did Rabbi Eliezer ben Hyrcanus die?

Question

In Moed Qatan 27a, a difference of opinion is brought between Rabbi Eliezer and Rabbi Yehoshua as regards the point at which mourners need to overturn their beds. The case is brought of Rabban Gamliel the Elder's death, and both Eliezer and Yehoshua inform the same group of mourners of their opinion. Those mourners follow the opinion of Eliezer, whom they refer to as an elder (זקן).

Rabban Gamliel was replaced by his son, Rabban Shimon ben Gamliel, who may have died during the war against the Romans. He was in turn replaced by Rabban Yohanan ben Zakkai, which might suggest (?) that his son, Rabban Gamliel of Yavneh, was at that stage too young to inherit the position of nasi.

Rabban Gamliel of Yavneh dies, according to Bava Metzia 59a, after Rabbi Eliezer falls on his face for tachanun - which means that Rabbi Eliezer (who was old enough to have been called an elder at the time of Rabban Gamliel's grandfather's death) survives Rabban Gamliel as well.

Are there sources that try to iron this story out and establish the relative ages of its characters at different stages? More specifically, are there any sources that indicate when Rabbi Eliezer died and how old he was at the time?

(I am asking because I am interested in understanding the death narrative of Eliezer ben Hyrcanus against the backdrop of the third revolt against the Romans and the death of Akiva, his student.)

Addendum:

@DoubleAA asks whether or not these are all the same Eliezer. The Eliezer in the Bava Metzia passage is Eliezer ben Hyrcanus. The Moed Qatan passage just says Eliezer. I tend to assume that stam Eliezer is Eliezer ben Hyrcanus, but obviously there's a precedent for seeing it as a different one (as in, for example, Berakhot 3a).

If somebody suggests that these are different Eliezers (perhaps in line with the tradition, recorded in Pirqei deRebi Eliezer, that Eliezer ben Hyrcanus was a student of Rabban Yohanan ben Zakkai), that would be very interesting. But either way, the question stands: are there sources that indicate how old Eliezer ben Hyrcanus was when he died, and when in history that occurred?

Answer 1

Rabbi Yitzchak Isaac Halevi in Dorot Harishonim, vol. 3, p. 356 writes that the gemara in Mo'ed Katan refers to Rabban Gamliel of Yavneh and the word "the elder" there is a mistake, as is evidenced by the version in Yerushalmi Brachot 3:1. This makes the story much more understandable, not just from the point of their ages, but also because, as Rabbi Halevi explained, Rabbi Eliezer lived in Lod and so did Rabban Gamliel at that time, so it makes sense that he would be the one to pass a ruling. Rabbi Ze'ev Yaavetz in Toldot Yisrael, vol. 6, p. 99 also asserted that the story refers to Rabban Gamliel of Yavneh (though there's a typo there - the secular dating should be 117 CE and not 147).

With that said, Rabbi Yaavetz thought that Rabbi Eliezer died in the year 117 CE, the same year as Rabban Gamliel (pp. 100-101). I'm not sure exactly why, but I would hazard to guess that it has something to do with the dating of the Qitos War and the time of the Martyrs of Lod. Similarly, and similarly-sourceless, Wikipedia says that R"G died because he was so distressed from that difficult situation.

As to how old he was when he died, I would guess at least 70-80. In Avot D'Rabbi Natan 6:3 it says he began studying under Rabban Yochanan ben Zakai when he was 22. By the destruction he was a close enough student and confidante of RYb"Z to have assisted his escape from Yerushalayim, so I guess he was his student for at least 8 years. Which means he was likely born by circa 38-40 CE. Add another 47-48 years after the destruction and we get to 77ish.