The Georgia Guidestones were unveiled on 22nd March 1980, midnight day marker was used while Alnilam, Belt of Orion was setting along the horizon in the West, link below:-
The Rosicrucian Fellowship's constitution dates from 8th August 1909. Ancient Egyptian day marker used being sunrise, Sirius rises with the Sun, link below:-
Astronomy graphs below:-
108 is also the number of major planetary years of the moon.
And explanation of the link between the moon and that number is given in a footnote of this book.
I remember other reasoning regarding the major planetary years for the moon but I can't recall where I saw it.
A decent link regarding some connections between the number 108 and various facts that would be of interest to the arcane minded.