Bathroom light not working but extractor fan is
SELV 12 means it is a 12-volt device.

Your "voltage screwdriver" is not suitable for testing low voltages like this.

The wiring should be as follows



Note this shows a main bathroom-light as well as a low-voltage light inside the fan unit.

Your pull-cord switch operates at 240VAC.

The Transformer does not supply power to the main bathroom-light. Only to the SELV light inside the fan-unit (where applicable).

The usual reason for lights not lighting is that the light-bulb needs replacing. You don't say whether you have replaced the bulb or tested it.

You can check the 12v connections using a more suitable voltage tester (with a 12V capability but safe for 240VAC)