I cannot find any reference to a 5.6L, but regardless, transmissions are not one of my specialty areas, so as Paul Harvey used to say, "I am going to have to tell you more than I know". To add to the misery, the wiring diagram shows the neutral safety switch as a mechanical switch, just like those that worked really well for the last fifty or sixty years, but they call it the "transmission range sensor", which implies it is a variable resistor, like a throttle position sensor. That type uses a computer to read the resistance value to know which gear you selected, but no computer is shown on the diagram.
We are going to have to approach this as if it were a standard starter system, and as such, given your additional observation of the gear shifter issue, the switch may be not being positioned correctly to turn on and allow the starter relay to activate. Try cranking the engine when the shifter is in neutral, drive, and reverse. (Do that with your foot on the brake, just in case the engine starts in gear)! If that works, I have solved your cranking problem, and we need to look at the shifter cable.
If you still have a no-crank, check fuse 21, a 15-amp, under the left side of the dash. That should have 12 volts on both sides when the ignition switch is in the "crank" position. If it does, this is where the multiple circuit versions start. Look under the dash where the clutch pedal would have been, for a small jumper harness that bypasses the clutch switch that isn't used with automatic transmissions. One wire going to it is white / pink and the other is dark blue / orange. The diagram does not show the color of the jumper wire. Back-probe that with a test light or voltmeter. You should again find 12 volts there when the ignition switch is in the "crank" position.
If you have 12 volts there, head to the starter relay at the right rear of the engine compartment. Remove it from its socket, then test for 12 volts on the four terminals. Be careful to not stick the test probe in so far that it stretches a terminal. That can cause future intermittent problems and you will have to come back to see me again. One of those terminals will have 12 volts all the time. Disregard that one. Of the remaining three, one must have 12 volts when a helper turns the ignition switch to "crank".
If you do find both of those 12 volts in the relay socket, move the test light's ground clip to the positive post of the battery, then we can test for ground. Probe the two remaining terminals in the relay socket. The test light should light up on both of them.
At this point you should have found something missing. If the first missing voltage was the switched 12 volts at the relay socket, the neutral safety switch is the best suspect, but we should perform one more test to rule out a broken wire before you spend money on parts.
Tuesday, November 29th, 2016 AT 2:20 AM