I am guessing for you to say this that you perceive desiring to understand why a certain thing is desired is equivalent to treating someone else as equal(?) That is, I'm a bit perplexed as to why you would think I'm treating God as an equal because I assert that He doesn't desire robotic obedience.

Does anyone have an example of a situation where obedience is rendered in spite of not knowing why it is required?

It was this implicit faith in God that made Moses what he was. According to all that the Lord had commanded, so did he. All the learning of the wise men could not make him a channel for God's working. But when he lost his self-confidence, and, realizing his helplessness, put his entire trust in God; when he was willing to obey Heaven's commands, whether they seemed to human reason proper or not, then the Lord could work mightily through him. {ST, July 12, 1905 par. 8}

What if, in the place of looking as Christ commanded them, they had said, "I do not believe it will do me the least bit of good to look. I am too great a sufferer from the sting of the poisonous serpent." Obedience was the object to be gained, implicit and blind obedience, without stopping to inquire the reason or the science of the matter. Christ's word was, "Look and live." ... {OHC 20.2}

None were compelled to look upon the brazen serpent. All could look and live, or distrust the simple provision God had made, refuse to look, and die. The people of God may not always see the reason for his requirements, and may not be able to understand his dealings with them; yet it is not their part to question and doubt his purposes. The lifelong recipients of his favor, they should yield him ready and willing obedience. All his commands are founded in infinite love and wisdom; and though we may not fully understand his purpose here, yet we shall know hereafter. {ST, October 28, 1880 par. 13}

Abraham might have pleaded that he was old and feeble, and could not sacrifice the son who was the joy of his life. He might have reminded the Lord that this command conflicted with the promise that had been given in reference to his son. But his obedience was without a murmur or a reproach. His trust in God was implicit. He did not stay to reason with his aching heart, but carried out the divine command to the very letter, till, just as the knife was about to be plunged into the quivering flesh of his child... {ST, June 2, 1887 par. 9}

Certainly this is important, but not for reasons of authority. It's not like the Army, where someone who is in command says something, and the underling does it because he is outranked.

Every good soldier is implicit and prompt in the obedience he renders to his captain. The will of the commander is to be the will of the soldier. Sometimes the soldier may be surprised at the command given, but he is not to stop to inquire the reason for it. When the order of the captain crosses the wishes of the soldier, he is not to hesitate and complain, saying, I see no consistency in these plans. He must not frame excuses and leave his work undone. Such soldiers would not be accepted as fitted to engage in earthly conflicts, and much more will they not be accepted in Christ's army. When Christ commands, His soldiers must obey without hesitation. They must be faithful soldiers, or He cannot accept them. Freedom of choice is given to every soul, but after a man has enlisted, he is required to be as true as steel, come life or come death.--Manuscript 7 1/2, 1900. {Ev 648.1}

He stood up proudly and urged that he should be equal with God, and should be taken into conference with the Father and understand his purposes. God informed Satan that to his Son alone he would reveal his secret purposes, and he required all the family in heaven, even Satan, to yield him implicit, unquestioned obedience; but that he (Satan) had proved himself unworthy a place in heaven. {ST, January 9, 1879 par. 9}

I don't think obedience is possible without understanding, so I wouldn't view this as a "requirement," in terms of, "I refuse to do this unless I understand" but it's a requirement in terms of God "requires" that we understand before we can obey; or, to put it another way, obedience without understanding is not something desire by God, nor of interest to Him, because He doesn't care for slavish, or robotic, obedience.

I wouldn't view this as a "requirement," in terms of, "I refuse to do this unless I understand"

I think I agree with your father, if I'm understand what you're saying correctly. That is, God doesn't require obedience before requiring understanding. ... But if he sees no reason to do something that he doesn't understand, I think he's right.

Jesus does not ask this sufferer to exercise faith in Him. He simply says, "Rise, take up thy bed, and walk." But the man's faith takes hold upon that word. Every nerve and muscle thrills with new life, and healthful action comes to his crippled limbs. Without question he sets his will to obey the command of Christ, and all his muscles respond to his will. Springing to his feet, he finds himself an active man. {DA 202.3}

Jesus had given him no assurance of divine help. The man might have stopped to doubt, and lost his one chance of healing. But he believed Christ's word, and in acting upon it he received strength. {DA 203.1}