Well, after a lot of troubleshooting on the wiring, I did not find any faults.
So, I looked at the ignition switch again. I discovered that the top plastic rotating plate on the switch mechanism was out of synch with the bottom copper plate. I accidentally stumbled across this when I turned it to the START position and it continued to click further clockwise instead of stopping. That was totally unexpected. I reinstalled the switch and sure enough, it worked. There must be a broken stop tab at the end of the START rotation. Anyway, I am not able to find a new 4-spade switch as they are no longer available. Instead, I found a 5-spade switch that will fit inside the key holder. All what is required is to make a short wiring harness between the new switch and the 4-terminal female connector at the end of the existing wiring harness and then route the new wires to the correct ignition terminals. The replacement 5 spade ignition is made by Standard Motor Products model US119.