The number seven is used in the Gilgamesh epos 40 times, so it seems more like a special connotation given to the number in general. Some examples:
You have loved the lion tremendous in strength: seven pits you dug for
him, and seven. You have loved the stallion magnificent in battle, and
for him you decreed whip and spur and a thong, to gallop seven leagues
by force and to muddy the water before he drinks;
If I do what you desire there will be seven years of drought
throughout Uruk when corn will be seedless husks. Have you saved grain
enough for the people and grass for the cattle? Ishtar replied. ‘I
have saved grain for the people, grass for the cattle; for seven years
of seedless husks' there is grain and there is grass enough.'
The next day also, in the first light, Gilgamesh lamented; seven days
and seven nights he wept for Enkidu, until the worm fastened on him.
Only then he gave him up to the earth, for the Anunnaki, the judges,
had seized him.
An explanation of your question is detailed here on the bottom of page 40 and page 41