Arthur,
I tried P and N positions several times yesterday and today, also moving the shift lever side to side in N as you suggest, with no improvement.

I assume the click I hear is the starter solenoid. The click comes from the engine compartment. Maybe I did not test with the lamp correctly. I connected the red alligator clip to the engine lifting ring, pushed the probe through the purple/white insulation, turned the key to start, and the light did not illuminate.

I got under the car and believe the locking ring on the NSS connection is OK. It is in the 'down' position. If I push it 'up' I can wiggle the connection, but in the down position, the connection is tight.

regards,
Mark