Should a Traditionalist accept Akita? Since it began in 1973, it is doubtful, since it says that we should pray for the "Pope"? Is it a legit apparition?

Akita is a stumbling block for sedevacantism.  There is nothing about the locutions
or the events or the visions of Akita that are doubtful for the Catholic sense,
especially due to the fact that it was examined carefully by the local bishop and he
gave his approval under ordinary jurisiction.  That is all that is necessary for the
Church to "apporove" an apparition.  What the "approval" consists of, is that "There
is nothing here in conflict with the Faith of Catholics, and this may be regarded as
worthy of Catholic attention."  It does not say that it becomes definitive of the
Faith or a dogma or a requirement or whatever.  It just says that learning about
the message is not a danger to your faith.  

But it is a stumbling block for sedevacantists.  They don't want to listen to what
the bishop has to say, because he's not a sedevacantist bishop.  Curiously, and
this is not a small point, there is no sedevacantist bishop who has now, or ever
will have in the future till the end of time (so long as he remains sedevacantist),
the jurisdiction necessary to render such an assessment of any vision, locution, or
phenomenon of any kind.  So don't bother looking for a sede bishop to give you
any clarity on this matter.  All he can do is run you ragged, round and round in
circles to no resolution.  That is the nature of sedevacantism.

Akita is a great example of a stumbling block for sedes.  It is probably the only
verifiable authentic apparition of Our Lady since Fatima.  Not to say there have
been no others, but there have been none that have received the Church's
approval is all.  Akita has been approved.  And for very good reasons.  All this
adds up to it being a great example.  

If you're going to throw it out because it fails the sede litmus test, then maybe
it's time to step back and take another look at the sede litmus test.

What about Fatima?  Maybe the Message of Fatima fails the sede litmus test too.  
Well, then you shouldn't add the Fatima Decade prayer to your Rosary.  And
you shouldn't be worried or even curious about the Third Secret, because it would
all be a deception of the devil and unworthy of your attention.  

By the way, that would mean that the devil inspired 3 innocent
children to heroic virtue and to live the rest of their lives doing
extreme penances after seeing a vision of hell and telling all the
world about it -- that would be the same hell that the devil wants
you and everyone else to disbelieve in its existence: check.  

And you shouldn't even be thinking about the Collegial Consecration or the errors
of Russia or the bad fruit of Vatican II or SSPX-Rome negotiations or just about
anything that happens in the News regarding the Church, because its all a
deception of the devil.

My one caution to you is, what are you going to do when the Pope and Bishops
of the world make the Collegial Consecration of Russia to the Immaculate Heart
of Mary one day (it doesn't seem likely it will be any time very soon) and Russia
converts and there is a period of peace that follows, as Our Lady promised?  

Are you going to say, "That's just a deception of the devil and I don't have to
believe it?"  

Remember there were those who accused Our Lord of casting out
demons using the power of the demons.  So this is nothing new.  

Oh, one more thing:  
You won't find any sede bishop or priest who can do an exorcism.  
Why not?  Because in order to do one you have to have local jurisdiction.
And if you try to do an exorcism without local jurisdiction you are taking
your life in your hands because the devil knows you don't have jurisdiction
and he most certainly will use that against you to the fullest effect possible.  

Even to your temporal demise, your "substantial change."

So if you have a problem with demonic possession, you're going to be stuck,
as a sede.  But wait......  There are no sedes with that problem, are there......  

Hmm..

I wonder why that would be?