So what do the specs on a neon sign transformer actually mean?

[Ben321]

Is the output voltage specified an end to end measurement? Or is it end to midpoint? Remember that most neon sign transformers are midpoint grounded. Also is the voltage an RMS measurement, or is it the peak voltage, or even peak-to-peak voltage? Also, what conditions are this measurement made under? Is it open circuit voltage? Or is it the voltage while a reasonable load (a neon tube) is attached?

Likewise with the current, is this the RMS, peak, or peak-to-peak current? And is this current measurement one of the short circuit current? Or is it the current when a reasonable load is attached?

[Gyro]

End to end. RMS, not that it makes any difference with a sine wave. Measured at rated current, which is at normal load, not short circuit. What you'd expect really.

[Stray Electron]

   FWIW ALL of the new-ish Neon Sign Transformers that I have seen are switcher power supplies and not just a big transformer.  I don't know what their output looks like. 

[Ben321]

End to end. RMS, not that it makes any difference with a sine wave. Measured at rated current, which is at normal load, not short circuit. What you'd expect really.

Actually it does make a difference with a sinewave. You have to multiply by sqrt(2) to get from RMS to peak. RMS has to do with heating effect. A 120v RMS ac source will heat the load just as much as a 120v dc source, due to the fact that the heating effect is based on average power, which is based on the RMS ac voltage.

However when you are talking about starting a gas discharge tube like neon, the peek voltage is more important. If a gas tube has a breakdown voltage of 5000v, that means the gas will ionize at either 5000v dc, or at 5000v peak ac. Not at 5000v RMS ac. 5000v RMS gives a peak voltage of 7071v. Remember that while heating a material takes a significant time (multiple ac cycles at 60hz), to ionize a gas takes only a few nanoseconds of exposure to a high enough voltage. So the peak voltage of the ac waveform is the most important value when talking about gas discharge tubes. I'm quite surprised to learn that the voltage on a neon sign transformer is the RMS voltage, not peak voltage, as neon sign transformers are specifically intended for running gas discharge tubes.