To answer the original question........................
First let me qualify that I am not licenced on the 777 or RR Trents.
I am licenced on 747 Cf6 Rb211 D4 and G2 and Jt9 (A while ago)
The FADEC engines RR G2, Cf6 do not have a flight/ground idle solenoid. To increase speed of the engine they just open the fuel valve accordingly until the desired N2 or N3 (according to engine) is achieved.
Hope this helps BelArgUSA.