The rear lamp is not for you to see but others to see you during
foggy situation (not much use in SG except maybe during rainy day )
for clearer visibility. Imagine what the driver behind you will
think if you have 2 fog lamps lighting up at the same time

Not sure what car you car you are having now... the 2 buttons are
placed next to each other in my car. Your car was mod. b4?