Not with you on that John. A digital meter will do the measurement just fine. They don't 'more often than not' show an open circuit on a continuous coil - at least none of the four such meters I have here does! (Nor does the analog one, perfectly true.) This applies to still-good original windings from eg Lucas, Bosch, BTH and the rest, as it does to rewinds.
The slipring to coil connection on rotating coil mags is a lousy bit of work really, but the push-fit has been with us as the standard method since before WW1, and never really got improved. A plastic grub screw (or something) might have been a good idea, maybe, but there's norralot of playspace and the angles of dangle are awkward.
Absolutely crucial to test continuity when fitting sliprings, as it's all too easy for there to be an open circuit, and then arcing inside the slipring, which does things no good. We want to see exactly the same resistance from armature earth (spindle) to brass on slipring as we see from spindle to the bare spike on the coil before the slipring is fitted. Always a very good idea to clean out a slipring that is to be reused with a small number drill - but better still to replace with a decent modern job, as they're not expensive in the overall context, and the dielectric strength of old ones may have degraded: putting seemingly-good ones in the HT line off a coil tester and heating the ring up will often show how badly, as the current required to get a spark through often goes much too high with temperature.
But I'm pretty confident I haven't come across a continuous coil which any of my digital meters shows to be open line. Hundreds of coils with a break will work on an independent tester due to the spark jumping inside, indeed they'll work often almost to the makers' specs (eg Lucas' "2 amps at break for 5.5mmspark across three-point test gap") which confuses things, but a break is a break for a' that as Rabbie Burns didn't say. And a break only gets worse until it doesn't allow the spark to get through.
Ref Richard's kind comment, not in the least in selling mode, honest! A WIMA 220nF job as fitted by Dave Lindsley and many others, the caps used by Andrew Beezermac, and the caps used by a number of others do a really good job. Rolled paper, ceramics wired or solder-mount, whatever. And some of the old mica ones from way back remain good almost indefinitely as far as I can see, having tested them from all eras, back 100 years or even more.
I have a graveyard of extracted modern capacitors chez moi, though (hundreds of, literally) and it is sadly the case that a lot of repaired mags with perfect rewound coils and other parts are let down by the use of capacitors which aren't that great in this application.
Whether that's the case here remains to be seen when other causes of grief have been eliminated. As I said, hopefully not, cos it's a pain in the backside to fix . . .