Use a voltage divider to monitor the 12V at the light bulb. Make the resistors large enough that they do not significantly affect the bulb. A 3K resistor for R1 and a 1K resistor for R2 divide the voltage by 4, giving you 3V at Vout when powered, and a 1K pulldown to GND when the switch to the light is open.

Use a voltage divider to monitor the 12V at the light bulb. Make the resistors large enough that they do not significantly affect the bulb. A 3K resistor for R1 and a 1K resistor for R2 divide the voltage by 4, giving you 3V at Vout when powered, and a 1K pulldown to GND when the switch to the light is open.

EDIT:

Note that the question was changed from "how to detect 12V turning on a light bulb" to the current question about doing so for a backup bulb in a car. Other solutions are better for an automotive environment.

Use a voltage divider to monitor the 12V at the light bulb. Make the resistors large enough that they do not significantly affect the bulb. A 3K resistor for Z1 and a 1K resistor for Z2 divide the voltage by 4, giving you 3V at Vout when powered, and a 1K pulldown to GND when the switch to the light is open.

Use a voltage divider to monitor the 12V at the light bulb. Make the resistors large enough that they do not significantly affect the bulb. A 3K resistor for R1 and a 1K resistor for R2 divide the voltage by 4, giving you 3V at Vout when powered, and a 1K pulldown to GND when the switch to the light is open.