I’m not sure what you’re reading into my posts.Agreed. I never said that. But your comments about Gad are clearly incorrect. They were under the Law whether or not they obeyed it and are clearly sons of Israel that came out of Egypt.
The Tribe of Gad was taken away into captivity by the Assyrians along with the other lost tribes. Most mainstream historians will say they mostly either assimilated into the Assyrians or were scattered here and there. Some far out theories will claim things like they’re the Irish, or the Tribe of Dan are the Danish, or they’re Ethiopians, and other off the wall theories with little or no bases in archaeology. Various nations and peoples want to think they are the lost tribes of Israel and that the blessings belong to them. It’s more likely then not just wishful thinking.
There were two Kingdoms when the Assyrians came through. The Assyrians conquered the Northern kingdom—Israel. The Southern kingdom—Judea was not conquered and the Tribes of Judah, Benjamin and maybe another one maintained sovereignty over the area around Jerusalem, Bethlehem, and Hebron. They may have become a vassal state at some point…? But they (Judah, Benjamin, maybe another tribe?) got to stay there and were never “lost” to history like the other tribes.
The Babylonian exile was later, and they came back to Israel after the exile was over.