Why is the Mashiach ben Yosef called "Mashiach"?

Question

I know that there is a concept of a Mashiach Ben Yosef and there is substantial discussion about whether he is an essential precursor to the Mashiach Ben David and what, exactly he will accomplish, but I can't figure out why he is a "Mashiach."

Doesn't the word "Mashiach" refer to having been anointed with shemen hamishcha, referring to kings and priests? A person who could be a mashiach would then have to be either from the Davidic line (the tribe of Judah) or the priestly line (the tribe of Levi).

Ignoring that the tribes from Yosef were among those lost in exile when the Kingdom of Israel was dispersed, so establishing anyone as a descendant (and still a knowledgeable and visible religious Jew) would be difficult, why would there be a construct which refers to someone not eligible to be anointed as "mashiach"?

Is the MB"Y just an exception, like Koresh, or does the term evolve into something which is not connected to anointing (the way Rashi reads Daniel 9:26, "the anointed one: Heb. מָשִׁיחַ. This is purely an expression of a prince and a dignitary.")?

Answer 1

Because Mohiach ben Yosef will be anointed/assigned to war [of Gog uMagog] (as one is said to be in Rashi's comment to Dt 20:2).

That is stated in Bet Hamidrash 6:96 (seven lines from the bottom):

...אף לעתיד לבא משוח מלחמה עתיד לעמוד מיוסף, ומשוח העומד מיהודה קשה ממנו, שנאמר (זכריה י') וגברתי את בית יהודה .

Answer 2

Well Mashiach ben Yosef will be a king for some time before Ben David arrives which fits the term of annointed.However when we refer to messiah this is a term deliberate to hashems mission of perfecting this world which initially was entrusted to Adam and he failed and corrupted the world further. So Mashiach Ben Yosef is a messiah to fix the corruption in the world Ben David is the Messiah to bring the world to its full perfection.