Good point with the switches.
I had left the DMM in DCV setting, switched to 20 MOhms and it also happened. Switched to Ohms range, back to DCV, and in the 20MOhms range and below nothing happened, only in the 2V and 200mV range settings the readings steadily raised.
Played back and forth with the DCV and Ohms mode switches to actuate them and hopefully clean a bit of eventual oxidation, and it got sporadically a bit better, but not on the last two lower ranges.
And this would not be like the normal voltage you measure with open leads, these would oscillate around some low value usually in the mV range- here I would be seeing numbers of >100Volts (theoretically) in the uppermost range, and after switching a range down, the exact same numbers would stay. (Only the decimal point would be moved at this then)