It took a while, but here is the first run of testing on "conductive" lubricants.
I limited the initial testing to products I could find locally which advertised in some way they were 'conductive'. These are Excelle Lubricants (Phoenix) XL Light "plastic compatible conductive model railroad penetrating oil" and Aerocar Conducta-Lube and Cleaner ACT-3753 (www.achlubes.com)
Testing was performed using a Cen-Tech 61593 11-function digital multimeter and its 'standard' probes. The 9V battery was replaced immediately before testing.
The lubricants were first tested for bulk conductivity. A true conductive lube or grease (e.g. one that is silver- or graphene-loaded) will exhibit very low bulk resistance. Conversely any hydrocarbon-based lubricant will have very little conductivity, on an order essentially indistinguishable from insulating lubricant for most model-railroading purposes.
The Cen-Tech meter features an 'audible continuity' setting and a measured (to within a nominal .02%) low range of 200 ohms. Neither of the test lubes possessed enough conductivity to display any numerical indication even at a probe-tip separation less than 1mm. Physical contact within the liquid gave an unsteady reading varying with angle and pressure between about .006 and .156 ohm observed, a confirmation that a liquid insulating layer was present.
In order to test sliding contact, I slid one probe along the shaft of the other, the contact area between two cylindrical shafts being reasonably comparable to a contact with rail. Dry, this produced relatively consistent readings between about .003 and .000 indicated. Applying the XL Light by dipping the probe tips in the bulk liquid, sliding contact varied irregularly between about .050 and .156 ohm, which would appear to indicate a reasonably good tribological film was formed (and was reasonably self-healing) on the metal surfaces, but no more conductive than comparable non-conductive 'nonpolar' lubricants.
Following the instructions provided by Aerocar, the probe tips were carefully solvent-cleaned and -rinsed with the recommended 91% IPA before testing the ACT3753. This product is also marketed as a rail-cleaner, and several small-tipped tools including a plastic-bristle brush are provided to facilitate this. I applied the product as for the XL Light, by dipping the probe-tip shafts in the bulk lubricant, with reasonably similar results (observed .036 to .126).
Interestingly, in neither case could I achieve the conductivity seen between clean probe shafts, which with only slight sliding pressure (as noted) could produce a .000 meter indication.
It remains to be seen if these products, the Conducta-Lube in particular, have a Wahl-clipper-oil-like limiting effect on conductivity loss in rail electrical contact over time or for different levels of corrosion, micropitting, and contamination. What is certain, however, is that they do not conduct electricity in any sense a hobbyist would call 'conductive'.