Sounds like Sir Chook knows what he is doing (I was trying to think of a chicken pun, but couldn't)

I would think there would have to be a condenser, otherwise the points would arc and bugger up very quickly.
Either there is a condenser (capacitor of some description) hidden back there, or we have inadvertently found why it ran for 40 seconds, then lost spark

A reading of 1 (infinite resistance) with the points open sounds about right.
$2 multi meters are the ones to get - I bought a $70 one from SCA (on special) because it was a Stanley - turns out Stanley USA allowed their branding to be used by a California Company TFT (Total, something, Tools) who make the cheapest crappiest tools in mexico and china.
Now I refer to that multimeter (with tach and other settings) as a Totally F***** Tool - dead 1 year and 14 days from purchase.
SCA wouldn't help, so I emailed Stanley, and they told me It's not theirs.