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.