@Ezekiel 33:3 Great info from your research. I am also going to post this to http://ahgamen.net and https://astrologyahgamen.milkyymedia.com/ The Magi visiting the Messiah, it is said, were guided by "the star". This has been a burgeoning question with no conclusive answer, there are many theories and beliefs. The Star which appeared over the region of Bethlehem, was it a star, as we understand stars today, or was it a planet, a conjunction of planets, or was it a comet? You mentioned Jupiter and Saturn which came up from your research. In my opinion, I tend to not put much emphasis on that pairing, since those two planets meet up every 20 years approx. Since the arrival of the Messiah was a rare event, I would think that whatever was the star, would only occur once every millennium or less frequently.
It is apparently the fact that these wise men (12 of them or less) were of the occupation of astrologers. Now that is not exactly like the astrologers of the present-day. They used a different method and also had a very different mindset and reception by the society around them. The astrologers were probably Chaldeans or Babylonians, or Chaldeans from Babylon (if that makes any sense - because what were Chaldeans?).
As a result of this basic premise, that they were astrologers, the entire narrative around their seeking of the Messiah by their following of stars, would seem to mean that they studied the positions of the stars and found out that there was a significant event to occur. That is essentially the work of the astrologer. So the transliteration of "following stars" or the star stopped over Bethlehem, could simply mean that they fine-tuned their interpretation of the astrological knowledge and determined the exact occurrence.
It is also important to note that they did not pinpoint Bethlehem until they consulted with King Herod; for he was the one who directed them towards Bethlehem and wanted them to look there. On the way from the Eastern region traveling westwards, they did not know the exact town. Also note, that we are assuming the locations of these two places, but none of that is conclusively proven. Those were locations and towns in the Ancient day and there has not been enough archeological evidence.