Measurement of highly resistive samples with Keithley 2182a nanovoltmeter
In the 2004 manual, page 3-8 discusses digital filter.  Is this filter turned off?  If this filter is in use, and set to 'repeating' mode, it may convert any random noise into strange jumps in readings.

Also in the manual, I see on page 2-9, the the internal A/D creates hundreds of nA on the input, and for high-resistance loads (or disconnected input leads,) creates significant millivolts artifacts.

It appears that this voltmeter is designed for measuring junction voltages on good conductors, and will produce unwanted noise if connected to high-resistance samples.

Test: disconnect the lemo jack, see if the unwanted signal is still there.  If yes, then it's caused by the meter itself.