Having showed the impossibility of "believing" something unconsciously, how about looking at the biblical teaching concerning "belief", particularly those things which belong to the non-corporeal such as a fiduciary faith/belief in God and Christ.

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Isaiah 1:18 (ASV) "Come now, and let us reason together, saith Jehovah: though your sins be as scarlet, they shall be as white as snow; though they be red like crimson, they shall be as wool."
Here, God is appealing to reason with a proposition to consider having shown that He will not have anything to do with the people of Israel due to their myriad sins. The call is to repent and embrace (believe) in the mercy of God. Certainly this involves a conscious decision.

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John 8:24-30 (ASV) "I said therefore unto you, that ye shall die in your sins: for except ye believe that I am [he], ye shall die in your sins. They said therefore unto him, Who art thou? Jesus said unto them, Even that which I have also spoken unto you from the beginning. I have many things to speak and to judge concerning you: howbeit he that sent me is true; and the things which I heard from him, these speak I unto the world. They perceived not that he spake to them of the Father. Jesus therefore said, When ye have lifted up the Son of man, then shall ye know that I am [he], and [that] I do nothing of myself, but as the Father taught me, I speak these things. And he that sent me is with me; he hath not left me alone; for I do always the things that are pleasing to him. As he spake these things, many believed on him."
Another appeal to believe using reason; a direct use of the intellect and the emotions/affections. Again, a conscious act of believing is called for.

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Romans 1:16-23 (ASV) "For I am not ashamed of the gospel: for it is the power of God unto salvation to every one that believeth; to the Jew first, and also to the Greek. For therein is revealed a righteousness of God from faith unto faith: as it is written, But the righteous shall live by faith. For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who hinder the truth in unrighteousness; because that which is known of God is manifest in them; for God manifested it unto them. For the invisible things of him since the creation of the world are clearly seen, being perceived through the things that are made, [even] his everlasting power and divinity; that they may be without excuse: because that, knowing God, they glorified him not as God, neither gave thanks; but became vain in their reasonings, and their senseless heart was darkened. Professing themselves to be wise, they became fools, and [ex]changed the glory of the incorruptible God for the likeness of an image of corruptible man, and of birds, and four-footed beasts, and creeping things."
Belief comes through the consideration of facts made known, either through perception or communication of thought or that which is inherently known. In this case, the wrath of God is clearly understood and acknowledged due to the incontrovertible reality of the everlasting power and deity of God is perspicuously seen in both the things which are made; the creation, and from an internal witness of conscience, man being created in the image of God. However, despite the overwhelming and undeniable witness of the truth concerning God men choose to deny God and the evidence that reveals Him. This denial, aka: unbelief is blatant, for they don't simply ignore the evidence but the exchange the truth of it for a lie, i.e., something of their own making, as they preen themselves on being 'wise', despite the fact that their belief is illogical and irrational.

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Luke 24:15-21,25,27,32-34 (ASV) "And it came to pass, while they communed and questioned together, that Jesus himself drew near, and went with them. But their eyes were holden that they should not know him. And he said unto them, What communications are these that ye have one with another, as ye walk? And they stood still, looking sad. And one of them, named Cleopas, answering said unto him, Dost thou alone sojourn in Jerusalem and not know the things which are come to pass there in these days? And he said unto them, What things? And they said unto him, The things concerning Jesus the Nazarene, who was a prophet mighty in deed and word before God and all the people: and how the chief priests and our rulers delivered him up to be condemned to death, and crucified him. But we hoped that it was he who should redeem Israel. Yea and besides all this, it is now the third day since these things came to pass... 25 And he said unto them, O foolish men, and slow of heart to believe in all that the prophets have spoken!... 27 And beginning from Moses and from all the prophets, he interpreted to them in all the scriptures the things concerning himself.... 32-34 And they said one to another, Was not our heart burning within us, while he spake to us in the way, while he opened to us the scriptures? And they rose up that very hour, and returned to Jerusalem, and found the eleven gathered together, and them that were with them, saying, The Lord is risen indeed, and hath appeared to Simon."
A marvelous and beautiful pericope that illustrates among many things that one can be plagued with disbelief but through knowledge of the truth one can truly abandon that disbelief and believe. In this case also, believing was conscious which resulted from a knowledge of truth and a desire to believe that which was hoped; a hope that was grounded in prophesy, a foretelling of the coming of the Messiah who would save His people from their sins.

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Acts 17:1-4 (ASV) "Now when they had passed through Amphipolis and Apollonia, they came to Thessalonica, where was a synagogue of the Jews: and Paul, as his custom was, went in unto them, and for three sabbath days reasoned with them from the Scriptures, opening and alleging that it behooved the Christ to suffer, and to rise again from the dead; and that this Jesus, whom, [said he,] I proclaim unto you, is the Christ. And some of them were persuaded, and consorted with Paul and Silas, and of the devout Greeks a great multitude, and of the chief women not a few."
Another instance of initial unbelief, which through the dissemination of the truth, many believed, i.e., they consciously considered (reasoned) what was said and deliberately embraced the truth of what was told them.

The call to repent, believe and follow Christ is always directed at one's intellect and often with an appeal to the emotive element of a person. The response, either to reject that call or to receive that call is always a conscious one. The ability to believe is another issue entirely not germane to this discussion. The reality is people believe or disbelieve something consciously.

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simul iustus et peccator

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