Flight at Night
FFF
I think that with further digging that you will find that the 30min rule is simply to define when the flight Rules; VFR/IFR can be/must be applied and the rule is taken with the surface as a datum.
The 12 degrees below the horizon (the horizon being the furthest point that can be seen) is to define the conditions that must exist for 'Night Training' to take place. As you surely know, at altitude it may still be quite bright although on the surface it is quite dark. This often catches many inexperienced pilots out. Having said that it is, on calculation, amounting to being the same for most of us. Sunset is defined as is twilight and therefore night. The rate at which we rotate and our movement around the sun would mean that thirty minutes is about equal to 12 degrees of change following sunset.
I'm sure that this will be explained better and that somewhere there is in the thomes the details that you seek. I wait with interest.