Yes, a common issue in all older cars (before ~2000) where the dash indicator is simply attached to the shifter. Later electronic displays are usually actual feedback from the transmission. Your only feedback is that NSS disables the starter circuit when not in P or N, that being "won't crank". Indeed, "no faint click from starter relay". When the relay does actuate, the downstream "contactor" within the starter makes a loud clunk and also moves the starter motor's pinion gear out to contact the teeth on the flexplate (or flywheel). When such recurs, try wiggling the shifter around "N" since you can go both directions there to hit the true "N" detent within the transmission. A common problem for owners of my 1985 M-B 300D since the plastic bushings in the shifter linkage fall apart to give slop.
I was once a bit embarrassed in 1994 when our 1965 Chrysler wouldn't start after church with several people watching me troubleshoot it in the parking lot. I had a multimeter and probed the terminals on the starter relay. Found the NSS wire wasn't grounded, as it should be when the transmission is in P or N. I thought "bad NSS?", but then peered in the cabin and found wifey who drove had left the shifter in "D". Everyone thought I was a genius to figure it out so quickly. Good we weren't parked on a hill, since I commonly find she also never sets the parking brake on most of our cars. She would be a true public menace if we lived in San Francisco. I am also emphatic that she align the stripes on the bathroom towels: