
10 Left AFT Fuselage
- AFT outflow valve
- Water drains, service doors, waste vents
- Air demand pump exhausts (2)
The only non-explicit hint in the flight manual is in the exterior inspection section above; searching the manual for "air demand" yields only one other result:
Sec. 6.2 Page 1 [...] Air Conditioning Packs
[...] Pack output is automatically increased during high pack demand periods (to compensate for a failed pack or recirculation fan), or limited during high bleed air demand periods (such as for gear retraction during takeoff).
Given the gear retraction remark, it must be related to the two "air driven hydraulic pumps" of the center hydraulic system. Knowing what to look for now, a Boeing paper on the 777's hydraulic system uses the engineering acronym ADP (air driven pump), which is not used in the flight manual:
[...] the EDP and ADP are interchangeable. The ADP is powered by the engine bleed air via the environment control system (ECS).
Using the engineering term to find photos yielded this from a maintenance manual, confirming they're the exhausts of the air used by the air driven hydraulic pumps:

— Boeing 777 "knocking" query, pprune.org
And this:

— reddit.com
This reminded me of the 767, which has one air driven pump, and sure enough, there is one such vent on the 767:

— airlinercafe.com