The next chapter of the mystery;
Lee Arnette found that 12 Volts were not getting to the brain box, therefore it wasn't sending the 5 Volts to the TPS, so the injector would only shoot and the engine would only crank sporadically.
Ignition module was good.
After we jumpered 12 V constant to the ECM, she would crank and run without issues. After about 20 minutes, the ECM started smoking. Put in another ECM and smoked it too. Conclusion is that we are dealing with a bad harness, which happens so often with the 84s.
Next step is to upgrade to an 85 or newer harness/distributor or maybe even go distributor-less.
More updates to come
BTW: Once it has an 85 or newer harness, the only thing remaining 1984 will be the chassis and the sail windows

\D