So that’s how you work out transformers. This is 1-ish ohm to 14-ish ohms - my DMM doesn’t seam that accurate - but my cheap Ebay transistor checker shows 3.2mH to 32.8mH which is close to 10:1.
It’s hard to find small transformers on the cheap sites, and even harder to get specs - my local only gives mH of the windings -, and expensive is kind-of a deal breaker because the whole timing-light is $27AUD.
I’ve got a 240V to 5V USB I can try, but like you said it needs an osc because it’s only 2 wire on the secondary.
EDIT - I just found 1 under High Voltage Transformer, it’s just that it’s 10KV. It has a lot of wires, so here hoping I can get to down to 300V.
https://www.google.com.au/search?q=Booster+Coil+Inverter&client=opera&hs=Mxz&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjU4azg7dnaAhWMvbwKHerNBpQQ_AUICygC&biw=1440&bih=803#imgrc=C-ipvtYqyQO8fM: