I searched solid states on this site--they fried Instantly. I'm sure there is an RFC circuit that could be put on the output of SS NST to prevent this
I'm not sure if the SS ones put out DC or hi-frequency AC, or what frequency. The Switchers I worked on ran at 15-25 kC. My TC resonates at 250kC, so a filter Is possible. Still, I think those SS units are Chinese made, now, and to save money, use light components and a current limit. They weigh
nothing compared to Transformer-type, so the ferrite choke or transformer inside is probably very small. It could also be they just can't work into a weird load like a Capacitor. I've heard of them firing a gap fine, but stop if a cap is attached. I thought they used voltage doublers to generate the HV, but that would mean a lot of bleeder resistors for safety. I need to find another and take it apart. It's too bad they won't do this--it'd be like a HexFet switching SS TC without the bother. I will Google it. But, any NST is designed for a "soft", slow turn-on and being left on 8 hours or so--not a sporadic, on/off 120 Times per second.My other concern is the "punch " to the SS circuitry. I worked on switching power supplies for a few years--these are simple higher voltage forms of one--so I am curious, too. The switchers we fixed simply needed a 1/3 load to turn-on and regulate. Then, the output caps soaked up any sudden loads. Linear supplies needed no load. Last SS NST I found I never tried, except in a friend's Neon Sign.
I'm sure this has been rehashed, but most NSTs that fail from T/C's get a little carbon track in the secondary. It can be fixed without rewinding. Chisel them open; freeze them overnight (you can do it Out Side in Minnesota right now!) and carefully chip away excess tar. Some try heating it in a barrel; do this Out Side city limits; art Night, stay Up Wind. It is a Mess-- Harry Goldman tried Once. Then, soak it a few weeks in kerosene (find a supplier, NOT a grocery store at $3/qt), or Diesel. Do NOT use gasoline or acetone as one old article in TCBA News suggested. Gas will take Insulation off older units!.) Newer NST's user Formvar, but don't risk it, anyway.) Then. brush as much tar as you can, an air tip helps but Sprays tar. Then, soak in alcohol a few more weeks and repeat. Then, immerse trans. in oil in a Tupperware container or something,.
EDIT: if you check under the heading:"HELP! My TC won't work!", there are two websites on basics of coils recommending not to use these SSNT's, or, Electronic Ballasts, as they are sometimes called.
Also,
never put Any type of NT
in Series--the insulation will break down, Put them in Parallel. It May be possible to remove tar from transformer-type as above and immerse in oil to prevent this, but it is messy. You only need 12 kV or so for a spark gap, anyway. Power is voltage times
Current, so I'm paralleling another 12 kV /30 ma to increase my output. Plus, real high voltage require even higher voltage capacitors, more expense or trouble to make them/series them. And, sometimes they charge unevenly in series; burning one, then, the rest out like a string of firecrackers. You always need equalizing resistors, more trouble/expense. I use 1000 ohms/volt, calculated on peak voltage of cap's rating plus 50% safety factor. Also, wattage is that peak voltage E squared/R, times 50%. I use wire-wound resistors, if I can find them. Carbons arc over. I try to string a lot of low wattage units to spread the potential out, then immerse in oil. I will try paraffin; I can't seem to keep anything sealed. So far, their has been No Problems this way.

.
The new transformer-type can screw up, too. Some have GFI inside, which trip or blow Instantly with RF. I know; I have an old Hyfrecator that puts out a wicked HF spark, and it frys those cheap Home Depot GFI's. Once, I though I had an open, and tore wires out, only to find they went
thru a GFI up the line--Bad Practice! They need to be dedicated for a single outlet, not in series. It may be possible to remove/bypass the GFI's in these new NT's. GFI's are only required for outlets near water--sinks,bathtubs, etc. Who puts a Neon Sign over their Toilet? ZAP!

GFI's are also notorious for tripping on refrigerators when they go into defrost. The ground is "floating" at this point,. A few quarts of melted ice cream later and I removed the GFI. Now, no trouble.

"Don't look for any sense to life, you will only Find futility."--DFS