I let the Sun illumination logger run for one day. It was a success, since it worked notwithstanding the wind that could have carried away the small solar panel. Basically I read the voltage across the solar panel that had a 4k7 shunt resistor.
These are the samples in graphical form:
Something doesn't look right: the steep edge both at "sunrise" and "sunset" on the solar panel. It's too fast, especially at sunset when the voltage dropped in barely two minutes. I suspect there is some heavy non-linearity within the solar panel.
The new strategy now is to measure both open-circuit voltage and quasi-short-circuit current at each sample. This process involves some form of switching (relay or MOSFET) and two ADC readings. But first of all I must do these measurements by hand with known illumination conditions. Upcoming Sunday is a good candidate day.