Bit of a scientific/historical mystery here: the ancient ever-burning lamps. Essentially, there are several accounts of these lamps that have ostensibly been burning for thousands of years without being refueled or burning out. I’m including a pretty thorough Reddit post below.
This is a great question. Like you, I am interested in this subject. One of my favorite archeological mysteries is the Baghdad Battery, because the jury is still out on their actual purpose. Something similar would be the Antikythera mechanism. It is a marvel to me that this type of technology was available during that era, and it makes me wonder where we would have been as a civilization if its use was not lost to time. Finally, I'll leave you with one more, a historical mystery, the Princes in the Tower. While the motivation for their confinement if clear, their disappearance remains a mystery.