Given this information, my wife would not deduce that All Israelites are descendants of Eber nor would she deduce that Descendants of Eber may or may not be Israelites but, rather, she would deduce that I do not love her anymore.
[/Variation on Monty Python]
I would assume that there were many descendants of Eber who were not descendants of Jacob. So are there (or were there) Hebrew peoples other than the Israelites?
If so who would be some examples of Non-Israelite Hebrews?
Well, I don’t think the Bible ever really adresses the subject, but several other nations in the ancient Middle East spoke languages very similar to Hebrew. The Phoenicians, for instance, and the Aramites (whose language eventually evolved into Aramaic).
I believe that the only specifically non-Israelite Hebrews in scripture are Rebeccah, her brother Lavan, and his daughters Leah and Rachel - in short, the people of Abraham’s homeland who married his descendents. Since Abraham supposedly came from Messopotamia, one might assume that Hebrews lived there, too.
First of all, the notion that “Hebrew” refers to the descendants of Eber is just a conjecture. But Genesis does mention many peoples who are descended from Eber but not Jacob. For example, Jacob’s twin brother Esau is said to give rise to the Edomites.