Israel's fall feasts look toward the Second Coming of the Messiah. In that regard I thought you might like to watch some online videos that look toward the rebuilding of the temple. The first is from last fall when work began on a full-scale replica of the temple in Mitzpe Yericho (a Jewish settlement near ancient Jericho) designed to help help future priests learn how to perform temple duties. The second is an interview with Chaim Richman of The Temple Institute on the work his organization is doing to research and reconstruct the various implements needed for worship in a rebuilt temple.
Some observations. First, these groups are legitimate in the sense that they represent a commitment to take seriously God's commands in the Torah regarding the proper way to approach Him in worship. Second, the groups are a small minority within Israel and don't represent the consensus of current Jewish opinion. (Most Israelis are not religious, and most religious Jews believe the temple won't be built until after the Messiah arrives.) Third, the Bible says there will eventually be a temple built, and God could use these individuals to accomplish His plans for the future. Finally, the Bible says the third temple will not be the final temple. A fourth temple (described in the Book of Ezekiel) awaits the arrival of the Messiah!