First trace setup:
- generator is a DG4102 (upgraded to DG4202), 8V max, 640mV min, 1Hz, square
- oscilloscope DS1054z (upgraded to DS1104z)
- probe at 10x, calibrated, tip is plugged straight into the generator's BNC, without any retractable hook or alligator wire
Second trace setup:
- generator is a DG4102 (upgraded to DG4202), 1.6V max (8V/2 because of 50 ohms terminator, x 10 because of direct cable), 128mV (640mV/10x2) min, 1Hz, square
- oscilloscope DS1054z (upgraded to DS1104z)
- direct 50 ohms BNC cable terminated with 50 ohms near the oscilloscope connector
It seems the culprit is the oscilloscope, not the generator, not the probe.