Constant resistance mode in electronic load
From the manual:
https://bkpmedia.s3.amazonaws.com/downloads/manuals/en-us/8540_manual.pdf
You need at least 1mA of input current for proper operation.  Your DVM does not supply that much for resistance measurements.
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How much current does your voltmeter supply?  It's not readily found.  However, I tried a simple setup here, and this is what I got for a 100 ohm resistor (0.3 mA):