Will a faulty 3rd brake light cause the brake light on the dash to stay on?
 

We just had the front and rear brakes replaced but the brake warning light is on again. I just realized the 3rd brake light on our 2008 Mini Cooper Clubman S is not working, so I am hoping that replacing this will fix it.

Anyone know if a faulty brake light can cause this brake warning light to come on?

Unlike before the service menu would say front and or rear brake, now it just says service and brake.