General Moderator Line of Succession
The General Moderator Line of Succession is explicitly stated in the articles of the Solemn League and Covenant to be a matter that the legislature shall determine. This has proven true to a further extent that was originally envisioned.
The little-used, mostly honorary office of President of the Convention, a relatively powerless interim official (generally a respected, elderly stateman) was initially the successor to the GM, to "carry on" single years of a GM' term. As each year drew to a close, the new President would assume the General Moderatorship. In fact when the office of President became vacant, the "senior senator" would take up said office. This caused a peculiar situation in the Crisis of 1875 because the then-President was killed in the same mishap as General Moderator McClellan, while there were two senators of identical seniority, leaving the position up for grabs. This was a very strange situation, one no one believed would ever occur again. So far, they have been proven correct. While the Cabinet tried to govern, ultimately they called a new election and the results were so close they required adjudication of the High Court.
When Bjørn Honstadt took over the General Moderator-ship in 1893, he tried to persuade Parliament to change the law about the succession, but they only agreed to hold a special election in the face of Honstadt's own failing health.
The office of the presidency was abolished during Great War I when two inept Presidents in a row nearly crippled America's war efforts.
Henceforth, Parliament decreed that should the GM become incapable of fullfilling his term, the permanent cabinet ministers would assume the office in order of what was perceived as importance--Foreign Secretary, Attorney-General, Chancellor of the Exchequer, Minister of War, etc. Thus Ruth Rosenberg was deliberately slipped into the slot of the Foreign Secretary as her husband's health took a severe turn for the worse. Two more Foreign Secretaries succeeded to the General Moderator-ship (Juanita Edith Baker-Stuart and Edward Moore O'Kinneide) until 1978, when James Wainwright helped pass a new Succession Act. His argument was that by having the Foreign Secretary the automatic successor, the new GM would of necessity tend to see his or her office in terms of international relations. Stuart and O'Kinneide seemed to be examples of precisely this, so the new Act specifically called for the GM to be succeeded by the Speaker of the House of Deputies (as Ronald William Regan did upon Wainwright's own death), then by the Speaker of the Senate, followed by the old succession order of the Cabinet.
So matters stand to this day.