depends on what you mean by 'starter relay'......every bike has a starter solenoid, which is basically the relay which allows current to flow to the starter motor directly from the battery. The GPz9 also has a couple of relays fitted to the main electrical board. These can get some serious corrosion issues for bikes used/stored anywhere near the coast.
The very slight dimming of the idiot lights when the kill switch is turned to 'On' - is 100% normal. What happens is that when you move the kill switch to the 'on' position, it switches battery current through the switch to the coils. The result is a slight reduction in the +12v signal to the idiot lights, which results in a very slight dimming and is not a sign that anything is wrong.
My guess is the words 'powder-coated frame' are the source of the problem. You need to make sure that every earth lead is working properly. When frames are powder-coated, this can often result in the new coating, preventing the earth bolts from providing a good solid ground connection. Check them all, especially the ignition coil brackets and the main earth lead from the battery to the frame/motor.
That is where I would be starting.
