My photographic memory is a wee bit low on film today and some of my film stock is a bit foggy.
Post the links to those schematics so others can follow.
As to chasing the goose. Way too many times without the schematic thatís what folks are left with. Very frustrating.
That leaves us to start at where we know problems start with the poor connections.
Those connections at the BCM are known to become corroded. Again this is not a 57 Chevy where everything was 12V or ground. So a simple probe light is no longer enough. With that said we are working on a computer controlled POS so all of those flakey grounds must be good or we start to run into the problems you describe.
So many of these connections are simple logic levels or GM LAN, network signals.
Disconnect your BCM connector another couple of times and remove the fuses clean the terminals and reinstall. The fuse terminals get pitted, build up a carbon track, then open the circuit. Even with a good fuse, if both sides do not make, contact......no complete circuit.
Now once you know a connection is good, repack, it with dielectric grease to extend its life it time between the next problem.
Pull up the schematics, I donít have them with me right now, and verify you are getting 12V power to the BCM.
Verify your fuses!!
Oh, on pin 62 on the BCM C2 is the 5V reference signal to the ingnition switch and 56 is the signal return to the BCM
This +5V on pin 62 with respect to Chassis Ground.
Then you will get different +voltage levels (0V-3V) on pin 56 depending on the ignition switch position, with respect to chassis ground.
Most of the schematics can be found in this thread
Now from Autozone here is their starter electrical wiring diagram
And let us know your progress