I strongly recommend to read the manual!
Ordinary DMMs have 10M impedance on all DCV ranges.
Bench DMMs usually only have 10M in 1kV and 100V due to the internal 100:1 divider, but the 10V , 1V and 100mV ranges have none, so these are really high Ohm, only pA input bias.
The KEI199 equivalently has 300V and 30V ranges with 10M and 11M, and 3V and 300mV are > 1GOhm ( see datasheet.
Therefore, it's completely normal that at this high input impedance, the readings starts floating.
At first, the input amplifier picks up any stray radiation.
Secondly, the amplifier integrates its own bias current into the input capacitor.
If you apply a bigger, known capacitor of say 100nF parallel to the input, you may calculate this bias current from the linear voltage change.
Frank