So many questios..but here is the deal ..

If you have 12v at those pins , then the criteria has been met.

So , is the 12v dropping b/c the BM is defective and loosing it ???

Or do we have a bad connection under the relay , or even the relay feed wire [terminal #19-gy/wt wire] at the Control module..[N3/1]
See where I am going here??

I would tie a couple of back probe wires on 85 and 86 and then put the relay in. I would then start the cold car and monitor those wires with your meter..if 12v is apparent and the pump does not come ON, the relay is not pullin IN ..simple as that.. and if you get 12v and it drops as soon as the relay tries to pull in, we have a bad connection somewhere between the relay and N3/1, b/c we have traced the circuit up to that point. [ that is what all that pin 2 and 86 to ground testing and stuff was all about. ]


Anyway, to continue..............................

I would verify the relay and I would verify the 12v.

On your other questions..open loop is the 02 sensors has not heated up enough to trigger closed loop and the AIR systems criteria is to STOP working when the sensor goes into closed loop.[ meaning, one of the AIR systems operation criteria is OPEN LOOP must be the condition..as stated in my criteria post] If No open loop, then no AIR.
The ONLY time the AIR comes on when 02 sesnor is in closed loop is when the Emmisions self test is done..and the reason they do it then is b/c they need a reading from the 02 in order to see if the exhaust goes LEAN when the self test energizes the pump for testing..if the 02 sensors was in open loop , it would not know what the exhaust condition was...OK???

Instead of the tutorials, lets just get on with the test..you will see how everything works when we have found the problem.. I have traced the circuit down on your schematic and we are completed all the way to N3/1 grounding, so lets just do a few more test and a few more readings..
Did you get your meters ohm function to work yet ??

..or I can send you the schematic.

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A Dalton