Nowhere in your post do I see you mention if the engine CRANKS .. Does it??
You mention it does not start, but "Start" to a tech can mean the car does in fact crank [ starter motor attemps to start car], but engine will not start
[ RUN]..
I mention this cuz E320 are famous for not starting due to a bad OVP.. but with a Bad OVP, the car will still CRANK.. but not START..
..if it does not crank, forget the OVP, as it has nothing to do with the starter circuit.
If the car does NOT crank, you are on the right track with the N switch. But if it won't start, but cranks , this is NOT the problem..
Anyway , the N switch white ring that you are turning is only the lock tab for the plug [ so it does not fall out..it is a retainer ring]
The terminals at the switch that should have continuity when the shifter is in N or P are #3 and#4 ..these are v/wt and v/grn wires . This is where an ohm-meter can be used to check for a connection/points contact. One may also just jumper these two and see if starter turns engine over w/key..that would indicate bad sw.
This cable also runs into the car, under the steering wheel/dash and can be jumpered there for testing.[ 4 prong plug. same #s]
The other 2 terminals are for back-up lamp..terminals # 1/2..

Et al.
The reason I mention the crank/start difference for posters is cuz the diagnosis of a starter circuit and a running circuit are so far in different directions that the first question you are going to get back from a Tech is
" Do you mean it just turns over and won't catch or do you mean it just does NOTHING? " ..from there , it is easy...