I did my usual research that makes more sense to me. According to the sefer, On Eagles Wings, by Hershel Brand, (published in 2002), Moshiach ben Yosef has one primary task to perform -- he will lead the Jewish nation in the wars that accompany the birth pangs of MBD, including the war of Gog uMagog. According to AbarBanel, Rabbi Akiva believed Bar Kochba was the Moshiach only because he thought he was Moshiach ben Yosef.
Because it was an accepted tradition among the Jewish nation that Moshiach ben Yosef will precede Moshiach ben David. He will not come to perform justice and charity, but solely to fight the wars of G-d and to take vengeance on their oppressors. (Abarbanel, Yeshuos Meshicho 1:4)As Bava Basra 123b states that "Yaakov saw that Esav's descendants could be defeated only by Yosef's descendants," and Bereishis Rabbah 99:2 supports, "In whose hands shall Edom fall? Those of the "Moshiach of war," who descends from Yosef." The era of MBY will be a time of great distress and persecution for the Jewish nation, culminating in the death of MBY during the battle against Gog uMagog.
Sukkah 52a states the following:
They will look toward Me because of those who they have stabbed; they will mourn him as one mourns an only child" (Zechariah 12:10). Why is there a eulogy? There was a disagreement between Rabbi Dosa and the Rabbis. One said [the prophecy refers to the eulogy that will take place] upon MBY's death.Rav Sa'adiah Gaon, in Emunos V'Deos 8:5 writes:
They also said that the catalyst for this will be the rise of a man who is a descendant of Yosef in Har HaGalil. He will gather the remnants of the Jewish nation and turn his attention to the Holy Temple, since Edom has taken hold of it. He will live there for a while, and afterward a man named Armelius will fight them and conquer the city, kill and take captives, and the man from Yosef will be slain. The nation will be beset by great troubles at that time, the harshest of which willb e the breakdown of relations between the Jewish people and all the nations [ to the point that the nations] will banish them to the desert ....The banishment to the desert may have been described in my post earlier here, which would be consistent with the quote above. The question arises "Why do we need two Moshiachs?" The answer is if the Jewish nation does teshuva, we don't need to go through the path of MBY, and will merit MBD immediately. However, if we haven't been doing teshuvah (just take a look around), the events of MBY will occur, and it looks to me like we have been heading towards this direction. Mrs Elyashiv's shiur only supports this belief of mine, with the exception that she believes MBD will arrive this year and fight Gog uMagog, which is inconsistent with the facts above.
Ultimately, Gog uMagog will be defeated in a miraculous way by Hashem Himself, as is explained in Zechariah 14. MBD is attributed by our Sages to fight his wars (againts the wicked among the Jews and the nations) without exertion, sword or spear. "He will strike [the wicked] of the world with the rod of his mouth, and with the breath of his lips he will slay the wicked" (Yeshayahu 11:4).
Now, I want to make a very "bold" prediction, based on women's intuition, which might be very wrong, but I'm going to say it nonetheless. I've been following Moshe Feiglin for a while. I do admire his courage in the past, speaking out against unjust policies set out by US pressures and against past US presidents. Amazingly, Moshe Feiglin was born in Haifa, and Haifa, is a city built on top of Har Carmel, part of the Western Galil. I think of all Jews, Mr. Feiglin, if he wins over the Likud leadership, is compatible with the role of MBY. Call me crazy, but it's just a woman's intuition. I do not necessarily support his views on everything, because I'm human and am faulty in every which way, but I think if given the opportunity to fight our battles against the nations, he will fit the role of MBY well.