Goldeneye's RNG
Goldeneye's RNG is built using a Linear Congruential Generator. The technical details really aren't important because it can just be thought of as an immensely long list of values. Each time the RNG function is called, the next value in the list is returned.
As such the RNG doesn't depend on any 'frame rules' as such, and doesn't directly use controller inputs to adjust its state. The unpredictability comes from the vast number of times that the function is called. Even in a 'quiet frame', the RNG will be called a couple of hundred times. Even in the menus the RNG is being called each frame, and in game a slight difference in lag will guarantee that the RNG will move to a different state.
It would be completely implausible to attempt to manipulate the RNG for anything which is determined even a little way into the level, for instance Dr Doak on Facility, who is placed once you enter the bathroom.
Even resetting the console in an attempt to just guarantee a specific cinema has not been attempted, though perhaps this is actually worth investigating for frigate 2.3.
