I've had many issues with electrickery on various ZXR 750 Ls & been able to sort 99% of them out, unfortunately I've never come across this one. The ZX7R & ZXR L wiring looms & electrical components are basically the same & even share some of the same part numbers for the hardware so the 7 probly suffers from the same issues as the ZXR.
I've found that the junction box (which houses the starter & headlight relays), starter solenoid & even the Ignitor box (A.K.A. CDI) can all have intermittent internal faults which make diagnosis virtually unpossible

The major earth junction hidden right in the middle of the wiring loom can suffer from dry solder as well which causes another intermittent fault. I'd hate to be an Autolec working on one of these.
That said, the best way to identiy the fault is to swap over the aforementioned components with known gooduns until the problem disappears, maybe a fellow KSRC member & 7 operator lives close to you & could hook you up (hook you up... fuck, I slay me

) Otherwise take the bike to a wrecker & tell them you want to buy an electrical component but you dunno which one so you need to do the above, they'll help you out because they know there's a sale in it at the end.
I hope I've been more help than a punch in the head but maybe less than an upside down American Bulldog