Phil – That is a really interesting observation.
I assume at the moment the spacecraft attitude will be quite stable. I don’t know whether the solar array can be steered to some extent relative to the bus but for now I would guess that they are keeping the spacecraft sun-pointing although I don’t know that for sure. If that is so then the brightness variations will be due to the phase angle (i.e. sun, spacecraft, observer). The repeatability here implies a diurnal variation. At the current range (about 1.2 million km) the Earth has an apparent diameter of 0.6 degrees so the effect of parallax on the phase angle is very small although certainly large enough to affect the timing of specular glints depending on where you are.
It would be very interesting to get two observers separated by a long baseline to do photometry at the same time. I suspect that they would see quite different profiles.
Once JWST goes operational the spacecraft attitude will be continually changing depending on the target so these glints will become much more (apparently) random.