I think dementia is part of the problem but he is able to carry on an intelligent conversation, read, and do his word puzzles. He is almost total care at this point with care givers around the clock. He seems to have his days and nights confused. He is a delight to be around and rarely complains. He and his wife drink coffee (albeit very weak) all day/night - they say it helps their breathing.
But chances are that at that age, there might be a number of prescription drugs involved, many of which have insomnia as a side effect. If so, that plus caffeine explains a lot.
What might be worth trying - if you haven't already - is prolonged release melatonin. Fact-wise: A - it is beyond question that we lose our ability to produce it with age, and B - mice get a 20% life extnsion from it.
There is a lot of info on "PubMed", and one study concludes:
"PR-melatonin results in significant and clinically meaningful improvements in sleep quality, morning alertness, sleep onset latency and quality of life in primary insomnia patients aged 55 years and over."
If the schedule he and his wife are on suits them, and they have round-the-clock caregivers, what is the problem? I would just try to schedule appointments at a time they are usually up and alert.
I have Delayed Sleep Phase Disorder myself, and I have been working with a sleep therapist to shift my internal body clock to somewhat more "normal" hours just for the sake of convenience. It is very hard work to make this shift! I would not bother if I were not working and did not have a spouse who needs caregiving.
If there is some benefit to "fixing" the timing of FIL's sleep, there are several good medical internet sites with suggestions. Try the Minnesota Regional Sleep Center, or Mayo Clinic. And giving up the weak coffee or switching to decaf might help. But it might also cause other problems, if they think it helps their breathing and it is eliminated.
Is FIL getting his medicines and pills OK inspite of his sleep schedule?