Maybe start with the basics; do you have a voltage (wrt to your ground) at the blu/wht wire? You may be on the "wrong" side of the lamp.
Alternator warning lights can be "different" in their operation. While some are a simple - sometimes relay controlled - switch, some are part of the regulator control circuit.
They can be switched on by removing a voltage - initially applied to either side of the lamp - rather than lit by simple switching to ground. What happens if you connect the LED light across the wires or PCB traces directly at the alternator lamp i.e. in parallel with the lamp? You may have to access the instrument cluster PCB for this.
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