Control Transient at Second Engine Shutdown
Second failed engine thrust would decay over several seconds - as the rudder is released from TAC offset, it would return to centerline just as the thrust from both engines approaches windmilling. I would expect a minor yaw wobble for a few seconds, but then the FBWire direct (alternate) mode would tend to keep the wings level and the pitch constant until airspeed decays severely, at which time (without pilot input), the pitch angle will drop in order to maintain a non-stall airspeed - maybe 180 or more knots. The FBW lateral law is mostly a rate system and assuming the yoke is centered, there should be only a minor bank angle. I also expect a phugoid pitch angle oscillation, but really not as severe as was reported by one 777 simulator user - perhaps only a variation from maybe 1500 to 3000 fpm down. This situation was probably not really flight tested and the simulators might be somewhat inaccurate.