Help with handlebar warmer wiring please

Just put on some new handlebar warmers from cycle country and I’m stuck at the wiring part. There is an included on/off/low/high push button toggle switch. NO thumb warmer.
Instructions state ‘connect the blue wire to the negative battery terminal’ which would go to the black wire on the battery. The other wire on the battery is red.

Right so far?

The only other wire is grey and should be ‘connect grey (positive) to a switched power source’.
This grey wire is right next to the blue one and not at all very long.
My questions:
1) how do they expect me to connect such a short wire to a switched power source?
2) what is a switched power source?
3) can I connect it directly to the battery?

So far I’ve routed all cables into the pod then the two power wires down to beside the battery BUT NOTHING IS CONNECTED YET.

Thanks for any help.