How the baterry warning light works....
When the ignition is switched on, live power travels through the printed circuit on the back of the clocks and through the bulb. From the bulb it exits down the blue wire from the clocks down to the alternator and pics up an earth though the alternator. When the engine is started and the alternator has been excited, the voltage increases and blocks the path to earth that the blue wires has/had. The alternator needs this signal from the bulb to excite the charge circuits.
If the bulb or wiring is broken then it won't charge.
Most common failure is on the push on terminal at the bacl of the alternator. Wire breaks and corroded inside the terminal.
Second is a broken wire in that area (near alternator).
Third is a blown buld.
Fourth is broken wire else where along the blue wire.