OK, I used the toolhead assembly instructions to see how the zero sense was wired in. Found at step 11 (“Zero volt sense harness installation”) https://ohai.lulzbot.com/project/mini-104-extruder-assembly/hot-end-tool-head-assembly/#step_11 that there is a specific lead that connects to nozzle on hot-end (for reference, it’s wired through Mini toolhead wiring harness at pin 16)
With my Mini powered off and unplugged, I used a DMM (mine has a specific “continuity/diode test” setting that conveniently beeps to let you know) to check continuity between nozzle and screw connector lead on hotend, and between that lead and wiring harness pins on the toolhead. And even from there to the bed leveling washers. Everything passed.
One thing i did find was that the nozzle needed some searching for a spot or my DMM probe to dig in before it would register sometimes, so this was a clue. I tried to rub some of the oxidation off nozzle, and flipped over the wiping sponge, and what do you know? Now it works fine. So I guess the essence of this trial is that when you have bed auto-level issue on first washer-- first make sure the nozzle is extra clean. 