Realist, let me start off by apologizing for not responding sooner. My health is weak and have not been on a computer since Wednesday.
Your question was: "Could you perhaps state all the real facts that support the idea of the GB being inspired by God?"
That is a very good question and one to think about. In ancient times it was fairly simple to see who Jehovah chose as leaders, for example Jehovah made many miracles showing that Moses was his chosen leader for the Israelites. Today, we are guided by faith since we have all of the inspired scriptures. I don't believe that the GB is inspired by God, but they are simply instruments that he uses in order to fulfill his will. Jesus the son of God said that the good news should be preached world wide. Jehovah has made sure that his happens, for he always give clear warning before acting against humans for their horrific and wicked acts. The GB is used to simply guide his people now adays.
In a Watchtower article it is written: " The committees of the Governing Body hold weekly meetings to review important matters, make decisions after prayerful considerations, and plan for future theocratic activity." After prayerful considerations, Jehovah does not inspire them to talk. When holy spirit is involved he will bless them on their research but will not give them word-for-word explanations .
Another Watchtower article mentioned: " Christian experience, guidance from the Bible, and the leadings of Jehovahs spirit direct this group of anointed Witnesses to theocratic conclusions on matters of great concern to the congregation. For example, in recent years the Governing Body has followed the Scriptural procedure in clarifying such matters as the Bibles view of "ministers," the God-given conscience, the carrying of lethal weapons, and the extent to which features of Isaiahs prophecy apply to the future Paradise on earth.Compare John 14:26; 1 Corinthians 2:10."
I think that statement answers your question. As regard to the visual proof that you ask for, I think you would have to clarify further was you expect Jehovah to show you as proof. Is faith in his inspired word not enough? Obviously someone has to take the lead in the preaching work and the GB does that. In the times of Moses, there were around 3 million Israelites, and Jehovah saw fit to organize them and Moses was their leader on earth. Although Jehovah guided him, on many aspects Moses made decisions himself. When judicial cases aroused, he would consult the law that Jehovah had given him and then made a decision. In that way, he was guided by Jehovah on every act. Now if Jehovah organized the Israelites and set up human leaders to guide them, would he not do the same now adays since were talking a lot more that 3 million followers? As we read the structures, we see that Jehovah usually follows the same pattern.
It is interesting that the leaders in the time of Jesus also requested a visual sign as proof that he was the Messiah, but Jesus did not give them a sign. Notice how Jesus responded:
"When evening falls, you are accustomed to say, It will be fair weather, for the sky is fire-red; and at morning, It will be wintry, rainy weather today, for the sky is fire-red, but gloomy-looking. You know how to interpret the appearance of the sky, but the signs of the times you cannot interpret. A wicked and adulterous generation keeps on seeking for a sign, but no sign will be given it except the sign of Jonah."Matthew 16:1-4.
Thank you for your question and I hope I've explained myself correctly.