Fuel Pump relay constantly clicking?

ok. I have a 95 buick lesabre and for a while it would cut off going down the road. When it was about to cut off it would like surge and the speedometer would jump and lights would flicker. Then i get it home and the next day or 2 the battery would be dead. Well when you turn the key to on, you can hear a constant non-stop clicking from the glove box area. I removed the glove box and found that it is the Fuel Pump relay that is making all the noise. Any suggestions or tips will be extremely helpful. Because i am not sure if it is the Relay itself or the box it plugs into. Could that relay kill that battery that quick and make the car cut off and do all the nonsense it does?