[alexwhittemore]

So when you're probing around the car without anything (major) running, you'd expect to see identical voltages even if the junction resistance due to corrosion is huge. It's when there's current flowing that you'd start to see drops.

Which is why it's very odd that you ARE measuring a drop at the DME. There's a definite possibility that you're not using sharp enough probes or pushing hard enough - what you're seeing could happen if your probes are measuring through a very high junction resistance, like they aren't poking well through built up grime and oxidization. That's the main reason good probes are super sharp. But it'd still be weird to see a noticeably slow build-up.

And you're right that sometimes you can see weird leakage effects where the device under test gets charged slowly by the tester, but CHARGING is almost unheard of - what you'll much more commonly see is a voltage falling as you bleed charge off a measured capacitor through the 10Mohm resistance of the meter. So what you're seeing on the DME is definitely something I'd consider odd. And if there's some other effect going on, not that I'm convinced that's even corrosion, it could definitely result in the brown-out you're seeing (although I'd be surprised if brownout to the one module resulted in the whole system momentarily shutting off.)