With this in mind:
Unanswered (by me) question: Is people’s use of time “approximately fractal” (which I guess you’d define as having a fractal dimension down to some length/time scale)? If so, does that mean that the TagTime algorithm is unfair, in the sense that, if say daydreaming happens approximately-fractally, it might be over-counted?
My intuition and subjective experience suggests the answer is no but I’m interested in what it would mean for the answer to be yes. Maybe you daydream every other second while working but that 50% work/daydreaming ratio is as efficient as your work gets. Zooming out, if you spend an hour working and an hour of dedicated 100% daydreaming then you want to consider that 50% working whereas TagTime measures it at 25%.
My feeling is that TagTime can accommodate that. If you consider intra-work daydreaming as part of your work process (which I would argue you shouldn’t but that’s a separate question) then tag it that way.
Would that solve it?
Maybe I should have posted this in the puzzle section 
I’m not worried that there is a serious problem of this sort for TagTime in practice, just curious.
What I’m curious about is: do the measured times depend on the characteristic time g chosen, in a similar way that coastline lengths depend on the length scale at which you measure them?
My understanding of TagTime is that it theoretically measures a point in time, not a period of time. You tell it what activity you were engaged in at the point at which you became aware of the ping. You don’t tell it what you were doing for the last 5 or 20 minutes. So I’m not sure the analogy with fractal coastlines holds. 
I bet I know how they measured it, too: sampling essentially the same way as TagTime does it 
I’m certainly not. But it’s not obvious to me that it doesn’t, either!
I assume all this is worked out in worthy mathematical texts somewhere, but I don’t know what they are.
Fractal dimensions are usually calculated as the ratio of the log of the relevant length to the log of the measuring tool, and you run into a distortion when the measuring tool length gets too small to be practical.
What’s the resolution of the brain’s perception of time? I dunno for you, but for this kind of thing, for me it’s on the order of at most a few seconds, and your tagtime measurements are more likely to be averaging every 15 minutes or something. When I tried using TagTime, I found in practice that there was a lowest level of resolution that was attainable on the order of perhaps 5 seconds. It pinged, and I needed to answer “what was I doing when it pinged?”, which tended to attach itself either to the most “worthy” thing I’d been doing in the 5 or so seconds before it pinged, or the most worthy of the things I was multitasking on at the time.
All of which means it’s not fractal: even if I took a tagtime measurement with a mean interval of everything from 60 minutes down to 60 seconds, it’d still not hit anything like the right kind of ratio against the actual phenomena to show fractal-like properties - the measured lengths (the numerator of the fractal calculation) would still be the same, while the measuring instrument length (60 mins down to 60s) would be getting smaller, so the ratio wouldn’t be constant, i.e. not fractal.
I think if you do that with 1 second instead of 5 seconds you can think of it that way. And 1 second is in fact the smallest possible gap between 2 pings.
But it’s meant to be “what is the focus of your attention at the exact moment you hear the ping?”