Well, let's begin by getting the text correct. It is only Mark's Gospel that contains the reference to the Son's ignorance.
Mk.13:32, "But of that day and that hour knoweth no man, no, not the angels which are in heaven, neither the Son, but the Father."
So, this is not a combined assertion; therefore it should not be overlooked to consider what MARK's special concern might be to include this unique comment.
Who does not know, and when does he not know it?
The Father knows. This is as plain an admission of divine omniscience as any. And Holy Spirit knows, because he is God, and the divine Son knows for the same reason. Nothing can be hid from God.
No man knows, nor can know unless it is shown him by special revelation.
No angel knows (which knows more than man by nature), nor can know what has not been revealed in the counsels of heaven.
No Son knows, but he
can know. The further question may be: in what sense does he not know, or why does he not know? Which answer may further yield the question: is it possible for the present (then) sense to change or the cause of his ignorance to change?
I've already explained in terms of Christ's ministerial exercise why he would not instantly know this fact according to his human nature. He conducted his ministry without availing himself of his full divine prerogatives, such as
turning stones into bread to satisfy his hunger. His estate was due to change once his work of self-immolation was complete.
It is the Person of the Father in whose will the Son is wholly given up. So, it is evidently the case that this information is not willed of the Father for the humiliated Son (as a man) to access, it not being consistent with his Mission to know it. It is holden, and the Son knows
that it is holden, and may even know
why it is holden. But he does not know what Holy Spirit has not willed to reveal to him, which restraint is an outworking of the pactum salutis, Father-Son "conference," in eternity-past.
One of Mark's unique angles on the Gospel content is in his presentation of the Son as a Servant quick to do his Father's will. He bustles here and there "immediately," not at all lazy but supremely active in his Father's service. The Son cannot do--nor is he expected to do--what he has not been informed or entrusted with doing, or relaying.
So this matter of not answering his disciples in this thing is not presented as his Kingly prerogative, or as "none of your business, I will attend to that." But, as the Servant and a man, it is not his place to know (then). The disciples hereby know, as Christ's own servants and servants of the Father, that neither in this life should they know "the day or the hour," if their Lord did not possess it while he was here. It will be unsuitable to ask him this question later on when his estate is changed (and they ask something like it in Act.1:6, and are not answered).