The crazy thing is that there was one more relay between the Starter Solenoid and the rest of the electrical harness.
I don't know it's function on the 3.1 TBI engine setup but this one was faulty. At this age it's possible to be some sort of alternative solution to an electrical problem of the past.
This is the reason I plan to have a through inspection of the electrical system on this car to check if everything is in place.