What's the immobiliser light on the dash doing? Is it normal or flashing an error?

Sounds like you might have a flat battery if its just clicking, rather than the immobilser. You may well have flattened it buy connecting up the wrong wires and causing a short straight to earth (a live to ground)?

First thing I'd try is detaching all three wires to the tail lamp, charge the battery and try and start the bike with the tail lamp disconnected. At least then you'd be able to narrow down what's causing the issue. Sort this first.

As for the brake switches (front and rear) not doing anything, I'd hazard a guess that you've connected the side light wire (blue/red) to the brake light circuit of the led lamp unit so it's at its brightest level all the time. Therefore, when you operate the brakes the lower brightness LEDs are illuminating, but you obviously can't see them, so it appears that the brake light switches aren't doing anything. Connect the LED unit directly to a battery using to establish which of the wires on it does the tail lamp and which does the brake lamp, then note it down.

Not sure why your XTX has yellow, blue and black/red wires going to the tail lamp? All XTs have yellow=brake (yellow/green on the Z), blue/red=tail and black=earth.

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