I am in possession of a 3600V 8mA neon sign transformer. This means it has peaks of a bit over 5kV, which is around the voltage of an electronic ignitor. This transformer can run 24/7 with a dead shorted secondary, and just get a little bit hot. This means I can safely put just about anything across its output. It also has an isolated secondary, which is important. Here is my plan for making this into a universal HID lamp ignitor:

For this explanation I will separate the secondary leads of the neon sign transformer into H1 and H2 just for clarity purposes, though there is no practical difference between the two.

- Connect the COM wire from the ballast to the socket's neutral connection (as per usual)
- Connect the H1 wire from the NST to the socket's neutral connection
- Connect the H2 wire from the NST to the socket's live connection
- Connect the LAMP wire from the ballast through a high-voltage tolerant switch to the socket's live connection

1) Starting with the high-voltage tolerant switch in the OFF position, power is applied to both the NST and the HID ballast. This strikes a low-current arc through the discharge tube of the lamp.

2) With the arc struck, the switch is then flipped to the ON position, applying the ballasted output of the HID ballast across the lamp (and also the secondary of the NST, which should be able to handle this at least temporarily). This ballasted output applied across the transformer would essentially just short it out, which is ok because it seems to have no complaints about being shorted.

3) Now with the arc properly struck, the NST is doing practically nothing, so its primary may be disconnected.

If I had access to a PSMH or HPS lamp I would try this out, but I own neither of those types of lamps. Do you think this would work? Obviously you might have to try flipping the switch a few times depending on what part of the AC cycle you flip the switch, but I think this would work. Ideally the NST wires and ballast wires would be phased so they are both positive and negative at the same time, but I don't really think that would matter if you got it the other way around. I could be wrong though. What do you think?

Getting a good high voltage switch capable of a few amperes of a HID lamp combined with >5kV withstanding and reasonably fast working is possible but not easy.

Also, while this may work for some lamps having low ignition energy like HPS, many lamps need a certain relatively high ignition energy and some OCV voltage presence with a low impedance at the same time to do glow-to-arc, likely this applies to metal halides.

Much easier is to wind your own superimposed transformer or borrow it from something that is not potted, like 150W electronic ballasts. Two or more of  identical transformers can be run in parallel for higher current. A primary of the ignition transformer can be driven by some trivial means (spark gap, SIDAC, etc)

In addition to what's said

Those transformers work at high frequencies, and the winding have sufficient impedance to support it

Connecting 50/60Hz voltage across its output is equivalent of connecting DC. The wire resistance of the secondary is probably a few kOhm to . With low frequency voltage in the order of ballast Voc or lamp Varc, it may dissipate significant power, possibly enough to be destroyed

Which gets me thinking, can this be overcome with a small capacitor in series (something suitable for the voltage, like a string of 1kV..2kV capacitors and equalizing resistors)

Winding a superimposed pulse transformer can be done with with ordinary ferrite cores of the order of ETD38, but some consideration must be made to insulate parts of the winding which are electrically distanced from each other (the wire enamel is not sufficient where turns from different layers may touch)

@RRK
I was thinking of possibly making my own switch, or maybe using a multiple pole switch with all of the poles in series to make a higher breakdown voltage.

I did not know that MH lamps needed "high ignition energy", that is news to me. I wonder why this is. If it comes to the point of me having to make my own ignitor circuit, at that point it is probably just easier to just buy the appropriate ignitor.

@Ash
The particular transformer I have is completely magnetic (60hz), just a high leakage autotransformer. I should have mentioned that in the original post.

I have several random ferrite cores that I salvaged from various switching power supplies that I could use for making an ignition transformer, but I probably won't end up doing that.

My idea is MH lamps typically have some amount of halide salts condensed on the electrodes. When the lamp attempts to ignite, these salts evaporate immediately and  fill the arctube with metal and halide ions. Halide ions seems to be quite good at quenching the discharge, likely by intercepting electron avalanches. So you often see when MH lamp flashes first on ignition, then goes out, then makes a few repeated attempts and only then establishes the arc. That way, igniting MH lamps needs some insistence with a dense series of ignition pulses having a certain energy. More, usually a presence of some open circuit voltage with rather low impedance is required to be applied together with ignition pulse series. Certain lamps even need a capacitor of a few microfarades that will discharge to the electrode gap at start to do glow-to-arc, automotive or entertainment electronic MH ballasts or ballasts for short-arc mercury lamps are including this!

@RRK
Very interesting theory, this would certainly make sense. I remember when I used to start up my 400W diazotype MH lamp that it would flash a lot before finally stabilizing. I first thought maybe it was just particular to that lamp, but I haven't had any other MH lamps to compare it to so maybe they all do that. Interesting