There is a big inconsistency in your argument: one one hand you say that the person's primary goal is to "confirm" whether the existence of God is true or not.
Therefore, having no evidence of the existence of God, does not mean the person "confirms" the inexistence of God. This means that believing in God without evidence or disbelieving in God without evidence (as no evidence can be provided of non-existence) should be indifferent for him,
So the additional implicit assumption in your model, is that not having a revelation from God equates to the person as evidence for his non-existence, which is of course no evidence at all, and therefore is a BELIEF that God does not exist if he does not reveal himself. Thus, it is not suprising that the outcome is the same : to not beleive, as this is his original (of the person) preference.