If it is an SU pump, it will always click. However the loudness of the click will vary from car to car. When you first turn on the ignition, you should get a few rapid clicks and then it will taper off as the floats fill up. There should be no more clicks until you run the car. As the fuel in the floats is consumed, the pump will run to refill them. This should only produce one click every few seconds, more if under heavier throttle. You may or may not be able to hear the clicks at all while driving but they are there.
If the pump is clicking rapidly all the time then you have a problem somewhere. The most common place is in one of the rubber inlet hoses between the tank and the fuel pump. Even a tiny crack can be the cause of this so if there is any doubt, replace all the rubber lines. If the lines are good, check for any cracks in the fuel pipes. You may not see a fuel leak even when there is a cracked line or fitting. Since the car does not stall, we can assume the cap is venting properly. The only other causes I can think of would be a fuel leak in the carbs or in the fuel lines after the pump (which you would detect by sight and smell), or a bad diaphram in the pump.