first thing i would do would be to buy one of these. they are of high quality and very legible a similar one for my '41 was indispensable in sorting out my wiring issues:
https://classiccarwiring.com/product...wiring-diagram
i suspect you own and know how to use a multimeter, as you've mentioned continuity...if not, then i would get one and learn how to use it.
continuity testing can be done with the battery disconnected. and should be all that's necessary to detect a short. i'd start with the headlights and search for convient and accessble places to place the multimeter's probes. they're even sharp enough to punch the a wire's insulation if necessary.
i wouldn't get too caught up in the voltage regulator issue, as its primary purpose is to maintain a constant output voltage from the generator or alternator. and only comes into play when the engine's running.