Mine sometimes shuts off before my basic phone is fully charged, because the current falls below the stay-awake threshold.
It seems to modulate charging current from USB with PWM operating at about 400 Hz. The small SMD below the SMD diode which is beneath the black wire in the product image photo is a 0.22 ohm sense resistor. The easiest way to observe charging behavior is to hook up your instrument across this resistor.
Solar cell is connected directly to battery through a schottkey diode. There’s a set of test points on panel itself on mine. I measured short circuit current at about 40mA in bright sunlight. I agree its useless. I think it does more damage than good by using it. Since you have to expose the whole thing to the sunlight, you will dramatically reduce the life of LiPo battery by exposing to such temperatures entire day at a time just to pick up 15% charge or so.