Neon does have some UV lines, but far down in the UVC part of the spectrum, so they will not pass the glass and be seen in this set up.
At 257nm, there are only three things which I know transmit it...quartz, water and air...and in air it is limited to how far it can travel...about 90% attenuation within 20 meteres I think.
At 186nm even air becomes an issue as this wavelength possesses enough energy, (see Plank's Equation), to break oxygen molecules into free atoms (which react with the O2 molecules to make ozone). At 170nm even water starts to become opaque and at 160nm quartz has gone black also.

I have always find light physics fascinating with all the materials use in transmission. I have took High Frequency System in one of the Electrical course a couple years ago and was able to learn that the impedance of the air is about 377 Ohms

How was that figure of 377 Ohms derived? Was it a capacitive reactance in some sort of unitary test capacitor, using air as a dielectric, or was it derived directly from the dielectric properties of the air.

As air is an insulator, this would not be a resistance...it would have to be some sort of AC reactance.....or was it the resistance per some unitary length of an arc's plasma in air?

No, Andrew. You can find this information at Wikipedia's https://en.wikipedia.org/wiki/Impedance_of_free_space The air is indeed one big capacitor between the vacuum and the earth ground. That's why we have lighting

Oh, I see, it is treating free space as a "transmission line"...so it is sort of like a transmission line impedance...