We're not geeks either! FU!
Harness usually refers to a wiring harness. From what I could tell from a quick google of it, on variable valve timing engines (most new engines) there is an adjustable solenoid or sprocket that responds to input commands from the cars computers, that adjust the intake and or exhaust valve timing. If it's the wiring harness that broke, and not the valves, solenoids, sprockets etc that broke, then it's arguably part of the electrical system.
From a consumer standpoint, I'd argue your powertrain needs it to work. From a manufacturer standpoint, they prefer it be grouped under electrical.
Somewhere that warranty must have literature that breaks down exactly what is or is not covered. If no such literature exists, maybe a lawyer or judge could convince them otherwise.