I think we've entered the Twilight Zone! 
Continuity and DC power test results understood on unit #1. Let's put that aside for now.
> Please confirm the two power terminals on units #2 and #3 are labeled A - U as shown in photos above (not U - A).
For unit #2 with the broken U terminal, I suppose it could be replaced/repaired...but to keep things moving, simply use the ACC GND terminal as a proxy for U. Based on your continuity test for #2, A = ACC PWR (connected internally)...this means U = ACC GND (connected internally).
> So you should be able to power #2 with DC+ to A, and DC- to ACC GND...and the unit should click. And if you reverse the power connections (DC+ to ACC GND, DC- to A), it should NOT work.
Assuming this is the case, we can then put unit #2 aside for now.
On to unit #3. You tested and found continuity between U, ACC PWR, NO and NC as depicted in Green above.
> This is a problem. Double check this. For example measure continuity between NO and NC. These should NOT connect together! Can you see any random loose strand of wire or whatever that might shorting the two terminals? Otherwise, the next step would be opening up the unit to find why NO and NC are tied together.
