Wait while we summon the UKGSER magic wand.
The general rule, & I'm not talking just ZZR here, is to disconnect ALL aftermarket electrickery first, leaving yourself with Kawasaki OE ONLY. Then you know everything you have is is fused - now check all the fuses are the correct values per the riders manual & replace as needed. That should narrow things down a tad. Kwak tuck the battery away awkwardly on these things IIRC - could there be an unfused or high rated fuse on say a battery tender flylead tucked away under the fairing somewhere.
Alternatively, could this just be road debris, even a plastic carrier bag, that has been flicked up onto a hot exhaust/cat/engine. The smell always lingers but usually leaves witness.