If you have the correct series resistor in in your string, all parallel neon strings will glow Provided:
You have about ~20VDC more then the minimum striking point of the worse string.
You have a supply capable of enough current for all strings.
So if your not "starving" the system with a minimalist approach or undersized power supply, all strings will light.
One of the ways you can tell if your current starved is: The cathode electrode is not uniformly covered in plasma or the plasma moves around the electrode in a small spot.
Illuminate the neon lamps electrodes with a 350 nm UV LED and the strike time will go way down. The strike voltage will be a few volts lower due to free electrons provided by the photoelectric effect :-) If you have an electrometer you will see a small current from your neon "photodiode", provided you only illuminate one electrode. However the mean free path is small in the lamp due to a high gas pressure and the current will be tiny compared to a phototube.
The purple glow during destruction is residual nitrogen released from the electrodes and glass envelope when overheated, coupled with a tiny bit of the sputtered vapor from the electrode metal.
As for inductive coupling, it was and is used for RF pumped fluorescent lamps used when the lamp is in inaccessible place and needs a long life. I used to have a full sized pyrex glass coffee cup with hollow walls, filled with neon. (Plasma Mug) You placed it on a inductive RF source pad with a high peak voltage field, and it lit. Was an Ebay item for a while, I don't know if they are still made.
Here is one cool induction coupled application of neon:
http://www.obsta.com/contents/balisor-for-high-voltage-lines/balisor-for-high-voltage-lines-2Maybe I need to shoot a video of the five pound bag of neon lamps placed in the microwave oven for a few seconds. :-)
Steve