It's probably CDI ignition .. or battery powered CDI. If not battery powered there will be a source coil (generates AC voltage for spark) & a pulser coil (tells the CDI unit to release voltage stored in the capacitor) in addition to the normal charging coil (which is actually on the same assembly as the source coil - just different windings). Could be TPI ignition too - that system has no source coil (uses battery power), but still uses a pulser for timing.. IF the coil has one connector & the coil is grounded to frame, it's CDI. If the coil has 2 connectors, it's TPI. The computer, or 'magic box' as I like to call it, switches the ground circuit to collapse the field in the coil with TPI -- with CDI the capacitor sends a large pulse the coil which passes thru the primary side of the coil to ground.
Normally on Jap machines, ignition parts rarely fail unless ridden in hot climates - like Phoenix for example. Lots of charging system problems out there ... but that's a different system altogether. CDI & TPI boxes hardly ever fail. On older machines you might fry a source coil, or have a pulser that quits. Ignition coils rarely fail either. On this thing it's a crap shoot. You could have multiple failures all at once, which is fun to diagnose.
I'd imagine their electronics are not as stout as the Jap ones.
But anyway, a source coil should put out at least 20 ACV cranking, pulser (or pickup coil - many different names for same part) should put out anywhere from 2 tenths of a volt to 2 ACV. If battery powered ignition (no source coil), battery needs to be fully charged or no spark. Grounds are very important on TPI - test them from the magic box for continuity. Check the kill switches - if CDI, when closed (to kill engine), they ground. If TPI, they open the ground to the box. Fairly certain most off road machines will be CDI though - so if that wire going to the kill switch from the box has continuity to ground, it won't spark.
I hardly ever do ohm checks, except with the ignition coil. 90% of the time the part will be in spec (like a source coil) ... then you check for AC output and you can clearly see it's toast. You can check the primary windings, then secondary windings, wire, and cap. On CDI from the connection to ground is primary, and from connection to the plug cap is secondary. Cap should have a resistor in it as well - sometimes those will fail.
Anyway I'm fallin asleep here so I'll check back tomorrow afternoon at some point to see how you made out.