The phrase "Absence of evidence is not evidence of absence." appears in Carl Sagan's The Demon-Haunted World from 1995. I don't know if he is the originator of that phrase or not, but he probably helped to popularize it. The phrase is very popular among religious believers and believers in other sorts of nonsense.
But it's clearly wrong. Absence of evidence is not proof of absence, it doesn't conclusively settle the issue all by its own. But it is certainly evidence of absence if the evidence could be expected to be there and is not.
- If we don't find any traces of the Israelites in the Sinai desert around the time of 1200 BCE, it is evidence that there were no massive nomadic wandering of Israelites as described in the Bible.
- If we don't find any trace of the earliest human evolution in Europe, it is evidence that the earliest evolution of humanity did not take place in Europe.
- If there is no trace of elves, apart from folklore, then that is evidence that elves don't exist.
But it's clearly wrong. Absence of evidence is not proof of absence, it doesn't conclusively settle the issue all by its own. But it is certainly evidence of absence if the evidence could be expected to be there and is not.
- If we don't find any traces of the Israelites in the Sinai desert around the time of 1200 BCE, it is evidence that there were no massive nomadic wandering of Israelites as described in the Bible.
- If we don't find any trace of the earliest human evolution in Europe, it is evidence that the earliest evolution of humanity did not take place in Europe.
- If there is no trace of elves, apart from folklore, then that is evidence that elves don't exist.