Follow up / expansion on the question:

Regardless of understandings of Genetics, this opens a larger question about the concept of identity and lineage that the writer of the epic held.

If my father is "Smith" and my mother was "Baker", would I have been considered half Smith and half Baker, or would I have been considered mostly Smith by ancient Mesopotamians?

2/3 seems like such a specific number. Is that normal for lineage in Mesopotamia or is that more to do with the God aspect?

Don't know if this is helpful, but in the realm of "myth", the number three often represents time: past, present, and future. This is usually tied closely with the number 4, representing space: north, south, east, and west. Similarly, 3+4=7, a number of completion, and 3x4=12, another number of completion. The entire Epic of Gilgamesh can be tied to astronomical events so it will be useful to look into an astronomical explanation tied to an 8-out-of-12 hour cycle (where 8 is 2/3 of 12). Or possibly 16-out-of-24 hour cycle, where 16 is 2/3 of 24. Alternately, it is possible this point in the story is tied to phases of the moon, in which case, Gilgamesh could be equated with the crescent moon: 1/3 visible and bright and 2/3 hidden and shadowy. In any case, look for a good reference that pulls in the astronomical parallels with the events of the Epic to learn the significance of the beasts, battles, and numbers in it.