Modern day world requires constant attention and effort. The leadership of a country and it's military need to be ready for anything at any time of day or night, and constantly man their posts.
Even short breaks should be limited.
Waking people up from their sleep, or engaging them in a situation when they are on vacation, only invites errors. Miscommunication, including insufficient details, especially, but lack of context and normal environment and materials can be a problem. And other things I expect.
In place of one person, a small group is in control at a given moment. An odd number to break voting ties. All decisions rest on this group at that moment. Individuals rotate in from the entire pool of presidents.
In extreme situations where one person needs to be the sole decision maker, one is appointed by the current group, or as a longer time frame is possible, more of the pool can weigh in. And the single lead person needs to hand-off the role to follow schedule.
I'm thinking this is a good setup - 4 hours "on-duty", 2 hours prep, observe current council, and get up to speed. After shift is to finish off, and integrate results into current status. This is primarily for the active leadership group.
Further, the pool rotates out to vacations, time off, and other functions.
Other functions besides the active leadership group are : public figurehead, diplomatic visitations, and further education.
Diplomatic visitations should be fairly clear, and will be a small fixed pool. In emergency situations, more can be pulled out of other functions.
Public figurehead is the appearing at traditional events, handing out medals, and other domestic functions carried out in the country.
Further education is intended to cover primarily new information, technologies, philosophies, and just general events and such. However should also be used for expanding knowledge into other common topics, even if not related to current activities.