I have been thinking some more about day to day life in the Fixed World, mainly because I am a player in Patrick's game, which is set in a world where it is basically always night.
The most significant logistical problem for anybody wanting to run a campaign in the Fixed World is sleep. In some places it is always night, in others always mid-day, in others always morning, and in others always evening. How do people figure out when to sleep in such a world?
It strikes me that things would work out as follows.
First, in ye olden times, people knew what the time was in their local region, but had little conception of what it was outside it. As far as you were concerned, in your village, there was morning, noon and night, and the sun moved around in its cycles, and you slept during the night time. The fact a few days' travel to the North or South the night would come slightly earlier or later depending on the time of year would be neither here nor there. You wouldn't care, because you would rarely leave your own village and the area around it.
So for the vast majority of the population, "when to sleep" is just a matter of local custom, determined by tiredness or some sort of arcane ritual. Perhaps the oldest person in the village decides, when he gets tired, that it is time for everybody to sleep. He gives some signal - rings a bell, puts up smoke rings, etc. - and that's the cue for most people to sleep while others keep watch. A big element of war would be trying to catch your enemies out when they are mostly asleep. Alternatively, a system might evolve in which the custom is that different people sleep at different times in a sort of rota: about a quarter of the population would be asleep at any one time, with the others hunting, farming, and going about their business. This means, of course, that there would be no downtime - work would go on continually.
The point is, it doesn't particularly matter that the people in village X have different sleep patterns to those in village Z. It doesn't concern them because they don't live in a world in which instantaneous communication exists, and for the vast majority of the time they exist in a purely local context. It would only chiefly matter for ports - you would get ships arriving without any idea whether the locals would be currently asleep or not. Ports would pretty much have to follow the sleep-rota model.
Planning would be extremely difficult, of course, because you wouldn't be able to say "I'll meet you in an hour" or "I'll meet you in the evening" - those concepts wouldn't really exist. Because the sun doesn't move, there are no hours. I think, probably, people would develop a very sophisticated understanding of other units of time - for instance, heart beats. Most adults' heart beats have an approximately similar rate. Because there would be no other way of doing it, I expect that people would have units of heartbeats - so while you wouldn't say "I'll meet you in an hour", you would say something like "I'll meet you in 100 time units", each time unit being 100 heart beats. It would be so crucial to be able to measure the world in this approximate way that people would be able to very accurately estimate what the real, "normal" heart beat rate was if, for example, they had been doing lots of running. They would be very good at roughly guessing how many time units are passing as they go about their business.
(This reminds me a little of Lewis Carroll's musings about the international date line.)
For kingdoms and empires, official measurement of time might be more important than simply figuring out when to sleep. Things like weeks, months and years are very convenient - it is hard to imagine people being satisfied saying "The Battle of Waterloo happened about 2 million hours ago." What you would want is a system of units: an A is 100 heart beats; a B is 10 As, a C is 10 Bs, and so on. And you would want to keep track of that in a standardized way. That would mean standardization of what a heart beat constitutes. It doesn't matter that the hoi polloi in the provinces use rough and ready rules of thumb. For official purposes there has to be a standard rate. And this would have to be the same wherever officialdom reigned.
I imagine a kingdom where the keeping of time is deemed important. Each major settlement is required to be on the same footing as regards when events have occurred or will occur. So they all need to have the same official heart beat rate.
How this is arranged is as follows. Some people exist whose reason for living is to provide a regular heart beat. These people are carefully selected when they reach the age of thirteen: every child is at that age brought to their nearest major town. There, if their heart beat happens to exactly match the required rate, they are immediately taken from their parents and sequestered as time pieces. They are from that moment forbidden to exert themselves in any way, and ensconsed in chambers where there is no external stimulus. They are kept constantly drugged with a special gas which regulates their breathing and prevents them from having any sort of emotional spasm which would cause their heart rate to fluctuate. They live in this way, in a sort of suspended animation, while their heart rate is continually monitored: there is an entire caste of monks whose job it is to take it in turns to sit and listen to the heart beat of the human time piece, all the while making small marks on a piece of parchment with each heartbeat. After 5,000 heart beats, the first monk steps aside and another swiftly takes his place to continue the marking. And these monks are surrounded by a host of neophytes and acolytes who constantly replenish the parchment and ink and carry it away to be officially counted. And in a room next door are the official counters, piling up all the many sheafs of parchment, each of which is marked 5,000 times for 5,000 heart beats. And each pile of 5,000 sheafs makes 25 million. And so on and so on. Entire rooms, warehouses, filled with paper, all marked with tiny stripes of ink, so that if anybody asks, they know when it was that such-and-such an event occurred - how many sheafs ago it was that the storm came, or the ship sank, or the meteor fell from the sky.....
Alternatively, a wizard does it.