I recall working on an arc lamp power supply, which used
> a spark gap for ignition.
>
> I wondered, and still do, are there any design techniques
> or formulas, to obtain a specific desired voltage pulse
> across the gap? Or is it cut and try, regarding the gap size
> and current? (the current break, that is)
You can buy high voltage spark gaps - the one I bought for that job in
1972 was glass-enclosed tube with an inert gas filling.
At the tine I'd bought a copy of a 1920's text book on the conduction pf electricity through gases, for which there was already a well established theory - search on Paschen's Law.
The arc lamp was exposed to the UV light from the spark, and that help start the lamp. The glass in the store-bought spark gaps wasn't UV transparent and the light they emitted didn't start the lamp nearly as often.