Heh, it's true, wiredgeorge has explained the turn signal system a couple other times in the past couple weeks, it's no wonder he's a bit tired of it.
It looks like what is really needed isn't more info about how the electrical systems work, but how to read the wiring diagrams and then troubleshoot ANY electrical system.
minutiesabotage, could you open up the Z1000K1 wiring diagram in the filebase and try to follow along? I could fish this one for you, but you'd only eat for one day... if you know what I mean.
On your wiring diagram, if you follow the grey and green wires from your turn signal bulbs back into the handlebar control you'll see they split into the hazard and turn signal switches in the control. That neither your hazards or turns work says there _might_ be a break from the handlebar control to the bulbs. There could be a break anywhere in there actually. The challenge is cracking your control open to fix it . You know, it may even be related to why you can't open it up.
Hope this helps.