Can you post a picture of this animal? Pictured below is an old HV neon sign transformer. The secondary voltage is 9,000 volts and as can be seen there are only two terminals. However, the HV midpoint is tied to the chassis ground. Either HV terminal to ground will yield 4,500 volts. Now in your case I just don't get this part:
PRI: 230V 50Hz 0.21A
SEC: 9mA 999V SEC: Uo 3130V
Maybe if you could post a picture it would help.
On another note, if the primary is 220 VAC and you apply 110 VAC you will get about 1/2 the output. The transformer really doesn't care. It is a ratio metric device so if you half the input voltage you half the output voltage.
If you are after a Jacobs Ladder there is no need to rectify the HV. A good source of a transformer like the ones pictured is a neon sign shop that may part with a used but working 9 to 15 KV transformer for a few bucks.
Ron