[abhattan]

Usually that "buzzing" noise is the relay opening and closing extremely fast. That means that it is not getting the correct amount of voltage or current. It might be a little difficult, but check the voltage going into it on the coil part of the relay. If it's too low, that's your problem. But the car has to be running. I somewhat of a current draw in my car which is similar. My dome lights come on whenever it seems that the car has enough juice. The buzzer changes tones as the voltage increases as well. I probably have current draw somewhere, but it's not bothering me right now. Let me know what you come up with.