For Minuteman I, the missile was physically rotated in the silo to be aligned with the target, using a day of surveying with the North Star as a reference. Minuteman II simplified this by rotating the mirror on the alignment block instead. This photo shows the alignment block and mirror on top of the gyrocompass. Note the warning label: the gyrocompass assembly and gimbals were made from toxic beryllium to save weight. 4/N
This diagram shows how the stable platform rotates along three axes. The window in the side of the stable platform allows the precise light beam from the "autocollimator" to bounce off the mirror. 5/N