@Dirk Some interesting thoughts. Now that the auto-fill is off, the mysteries ~150 gallons each morning is indeed gone. Going to let it go for a few more days, then turn it back on and check again.
I did do the math, and give my pool's surface area (794 ft²), an evaporative loss of 0.25 inches translates to 124 gallons ((0.25in / 12) * 794 * 7.48). Since I'm in Sacramento and the climate is fairly dry most days, this makes a bit of sense. I am a bit surprised if it's waiting to do all of its refill at one time, though. It's not always >100 either. Recently the weather has been getting much more humid, and I saw a loss of only 85 gallons during that time.
I guess our climates
could be different enough. I just know no fill water has been added to my pool in at least three months. Not a drop. I have a, let's just say, unorthodox level monitor, that gives me a visual readout of my water level above the bottom of my skimmer opening. For three months it hasn't been below 4.5". Right now, with some recent rain, it's back at about 5". It never gets higher, as it drains off through my overflow.
Some water is, of course, evaporating, but it's so little, and is being replaced by rain, and we haven't had much. Like I said, I suppose our climates could be different, but by how much? I am using zero water from the street, and I regularly watch excess drain off.
3.5" is where my auto-fill kicks on. 5" is where my overflow drains off water. My pool hasn't been below 4.5" for many months. My auto-fill has been shut off all that time.
Was your auto-fill off when you did the bucket tests?
You could rig up something similar. Tape a ruler to your edge tile. With your auto-fill off, your 1/4"-a-day theory should be easy enough to prove or disprove. Do a bucket test at the same time. Put a ruler inside the bucket, too. If it is evaporation, both rulers should track the same loss.
Did you mention? Is your auto-fill valve like a toilet tank fill valve? That's what I have. If yours is like mine, it's not filling every time there is the tiniest drop in level. There are thresholds (for lack of a better term). The level drops quite a bit, then the valve kicks on. Then the valve stays on for a while, even overfilling a bit, then shuts off. I don't know the measurement of the difference in water level this translates to, but it could be a 1/4" easy. I hope I'm explaining that well enough.
Now why that would happen at about the same time each day is still a mystery, but it could be air temp related. Or pressure related. That's why I asked about the morning shower. I don't know this for sure, but I suppose a sudden drop in pressure on the auto-fill valve, caused by a weak pressure regulator and a shower or toilet flush around that time, might trigger the auto-fill valve. Then once it gets going, it stays open for that 1/4" refill. Really just guessing here. But it could be something as simple/complicated as that.
Do you know? Do you have a backflow preventer connected to your auto-fill line? They trigger based on the pressure differential between input and output. That could be part of the equation.
Do you have any symptoms of a bad pressure regulator? Low pressure? Significant pressure drop at one faucet when another is turned on? Banging/clanging noises?