I know it don't have your exact problem! But in this case it's going to be more of a guide to hopefully help figure something out in this odd case. There is one step in there that might help lead you to where the interlaying problem lies.
And yes, by falsifying the sensor with a screwdriver vs turning the rotor wheel will trigger the coil to fire as it thinks the rotor is turning. With removing the White/Green wire is removing the signal wire to first the module then to the coil via the gray wire. Even using the screwdriver, the coil should only fire once per pass/swing of the screwdriver...Not continuously.
In the middle test where it says strike the White/Green wire to ground... As a test/in this case you'll want to try striking the wire multiple times by hand, and also try just holding the wire there to ground to see if the coil is still firing. It should fire during the strike but it should not fire held to ground. I'm thinking possibly/just maybe if the coil happens to keep on firing held to ground then maybe while it's odd it is the module.
Test # 2 to try... Remove the white/green wire form the distributor sensor, remove the gray wire from the - side of the coil and run a jumper wire between the sensor to the - coil and see if the coil fires/continuously.
OK I performed these tests and here's what I found:
The "middle" test, First time I did this, I get a single spark each time I tap the green/white wires together. But also get multiple firing if I hold the wires together. It does nothing tapping or holding the green/white wire to ground.
Test #2 also does nothing.
Next I tried to see with an analog voltmeter the signal coming from the green/white wire while flagging the sensor with a flat blade screw drive. I couldn't see anything, even with the volt meter set all the way down on the 0.25 volt scale, no meter deflection at all. (sorry I don't have a test light for this)
Next I tried the middle test again. But this time I no longer get the multiple firing when holding the green/white wires together. Only once when they initially touch.
So, since it's no longer showing the problem, I wonder if by flagging the sensor with the screw driver, after tapping it many times, and the problem now appears gone, if the sensor is flakey and now functioning correctly? Or maybe disconnecting the gray wire somehow "reset" the TB module or something?
I haven't tried to start the engine, but I'll put muffs on it and try that next to see if the problem is gone. If so I still have a problem just waiting to return...
Update: I just tried to start the motor and all it does is crank and crank and I confirmed I'm not getting any spark now. This I have seen before when I replace the ignition sensor a couple years ago. I'm almost certain that is what is wrong and it has gone from flakey to just dead. If that's the case, I'm very disappointed in the Sierra replacement part I just purchased two years ago. The original lasted almost 30 years.