There have been 3 attempts (132-135 ad, 363 ad, and 614 ad) to rebuild a 3rd temple by the Jews. All attempts failed.
Here is a very interesting historical account. Around 363 AD Julian the Apostate commanded to the Jews to rebuild the temple as a means to oppress the Christians and falsify the words of Christ.
Socrates and Sozomenus Ecclesiastical Histories
"Though the emperor hated and oppressed the Christians, he manifested benevolence and humanity towards the Jews. He wrote to the Jewish patriarchs and leaders, as well as to the people, requesting them to pray for him, and for the prosperity of the empire. In taking this step he was not actuated, I am convinced, by any respect for their religion; for he was aware that it is, so to speak, the mother of the Christian religion, and he knew that both religions rest upon the authority of the [biblical] patriarchs and the prophets; but he thought to grieve the Christians by favoring the Jews, who are their most inveterate enemies.
But perhaps he also calculated upon persuading the Jews to embrace paganism and sacrifices; for they were only acquainted with the mere letter of Scripture, and could not, like the Christians and a few of the wisest among the Hebrews, discern the hidden meaning [the allegorical meaning, through which the Christians could prove the validity of Christianity from the Old Testament].
Events proved that this was his real motive; for he sent for some of the chiefs of the race and exhorted them to return to the observance of the laws of Moses and the customs of their fathers. On their replying that because the Temple in Jerusalem was overturned, it was neither lawful nor ancestral to do this in another place than the metropolis out of which they had been cast,
he gave them public money, commanded them to rebuild the Temple, and to practice the cult similar to that of their ancestors, by sacrificing after the ancient way. [Sacrifice was permitted by Jewish law only in Jerusalem.] The Jews entered upon the undertaking, without reflecting that, according to the prediction of the holy prophets, it could not be accomplished. They sought for the most skillful artisans, collected materials, cleared the ground, and entered so earnestly upon the task, that even the women carried heaps of earth, and brought their necklaces and other female ornaments towards defraying the expense.
The emperor, the other pagans, and all the Jews, regarded every other undertaking as secondary in importance to this.
Although the pagans were not well-disposed towards the Jews, yet they assisted them in this enterprise, because they reckoned upon its ultimate success, and hoped by this means to falsify the prophecies of Christ. [Since Jesus in the New Testament had prophesied the destruction of the Temple, its rebuilding would make of him a false prophet.] Besides this motive, the Jews themselves [relying on the sympathy of Julian] were impelled by the consideration that the time had arrived for rebuilding their Temple."
Notice what happened when the Jews and pagans began to rebuild the temple: earthquakes and fires preventing the construction.
"When they had removed the ruins of the former building, they dug up the ground and cleared away its foundation;
it is said that on the following day when they were about to lay the first foundation, a great earthquake occurred, and by the violent agitation of the earth, stones were thrown up from the depths, by which those of the Jews who were engaged in the work were wounded, as likewise those who were merely looking on. The houses and public porticos, near the site of the Temple, in which they had diverted themselves, were suddenly thrown down; many were caught thereby, some perished immediately, others were found half dead and mutilated of hands or legs, others were injured in other parts of the body."
"The Jews, I believe, were just in this state; for, instead of regarding this unexpected earthquake as a manifest indication that God was opposed to the re-erection of their temple, they proceeded to recommence the work.
But all parties relate, that they had scarcely returned to the undertaking, when fire burst suddenly from the foundations of the temple, and consumed several of the workmen."
Your assertion that a 3rd temple would disprove partial-preterism and prove dispensationalism is an interesting one, considering Julian the apostate and the surrounding pagans wanted to build a 3rd temple to disprove Christianity, and make Christ out to be a false prophet. I also find it interesting that despite history showing multiple failed attempts to build a 3rd temple, in addition to Jesus stating that Jerusalem would no longer be the center of worship, the dispensationalists are still pushing for a physical temple.
john 4:21-24 Jesus said to her, “
Woman, believe me, the hour is coming when neither on this mountain nor in Jerusalem will you worship the Father. You worship what you do not know; we worship what we know, for salvation is from the Jews. But the hour is coming, and is now here, when the true worshipers will worship the Father in spirit and truth, for the Father is seeking such people to worship him. God is spirit, and those who worship him must worship in spirit and truth.