We had that discussion over in the Super LTZ1000 thread.
There, the original LTZ circuit was affected by any SMPSU, including 'modern' LED illumination.
Latter lamps don't have any EMC shielding, and are REALLY noisy, and I really wonder how these ever get a compliance certificate.
The x kHz EMC radiation is induced into the supply and output cables of the instruments, even twisting and shielding does not help.
That RF is then rectified in the LTZ transistors, which leads to a shift of the oven temperature, or caused frequent spikes and dips in the output voltage, in the range of several µV, or ppm.
The successor of the 332/335, the 5440/42, is practically immune to such EMC radiation, as well as the 3458A, when 10V are applied from the calibrator.
Therefore, I assume that the old design of the 332/335 is susceptible to disturbance, similar to the LTZ circuit.
Latter can probably be hardened against EMC as well, by adding some blocking capacitors parallel to these sensitive pn junctions, but I can hardly guess, which one.
The possible circuits, like the reference, the chopper amp, and the other module, are so big, that they can easily pick up any disturbance from the output jacks.
You may try to identify the root cause by directly measuring the +15V reference voltage with and w/o LED illumination.
That's accessible inside, labelled as Master Ref Test. Please do that testing in the 10V range only!
As the easiest solution, what I also have done in my lab, I recommend to remove all SMPSUs, and use regular incandescent, or fluorescent lamps running directly on 50/60Hz mains only. Where you can't avoid SM PSUs, at least watch out for EMC 'stinkers' inside your PCs / laptops, which also might radiate excessively, especially if after years the snubber capacitor has died.
By these two measures, i.e. no SMPSUs, and use of blocking capacitors, it is now possible to make sensitive and stable DCV measurements in the sub 0.1ppm range.
Frank