I am reading The Oxford History of the Biblical World.

A few interesting points. There are parallel stories. One of the most surprising is that from the Song of Deborah you count 10 tribes, not 12. Of which 2 are not considered tribes generally.

From Judges 5:14

14 From Ephraim they set out[e] into the valley,[f]
    following you, Benjamin, with your kin;
from Machir marched down the commanders,
    and from Zebulun those who bear the marshal’s staff;
15 the chiefs of Issachar came with Deborah,
    and Issachar faithful to Barak;
    into the valley they rushed out at his heels.
Among the clans of Reuben
    there were great searchings of heart.
16 Why did you tarry among the sheepfolds,
    to hear the piping for the flocks?
Among the clans of Reuben
    there were great searchings of heart.
17 Gilead stayed beyond the Jordan;
    and Dan, why did he abide with the ships?
Asher sat still at the coast of the sea,
    settling down by his landings.
18 Zebulun is a people that scorned death;
    Naphtali too, on the heights of the field.

So that gives

  1. Ephraim
  2. Benjamin
  3. Machir
  4. Zebulun
  5. Issachar
  6. Reuben
  7. Gilead
  8. Dan
  9. Asher
  10. Naphtali

 

Gilead and Machir are not usually considered tribes, and this list is missing:
Manasseh
Judah
Gad
Simeon

And Levi, though Levi is not usually considered one of the twelve. So is this an older list from further back?

Some interesting points the book make that argue for true memory in these stories is the fact that none of the ancient names – Abraham, Isaac, Jacob etc have YHWH in them. This is much more common later. Also that many of these characters do things later banned by the law – Abraham planting a Tamarisk tree (Gen 21.33), later banned in Deut 16:21 and Jacob marrying sisters (Gen 29:16-30), later banned in Lev 18:18.