Open the relay and look at the backside (foil side) of the internal printed circuit board. Both actual relays are mounted to this PCB, as are the lugs that fit into the harness socket.

The automated soldering process used in manufacturing requires a different type of solder than normally used on an electronics workbench with a soldering iron. That type of solder tends to crystallize and crack after a few years. Heat and vibration accelerate the degradation.

You can sometimes see hairline cracks around the heavier soldered connections.

The first image below shows the same problem but in an OD relay, the second image shows it after resoldering. I show these just to illustrate what bad and resoldered connections look like. Your fuel pump relay looks different inside but the cracks at the larger connections would be similar. The third picture below shows an OD relay open (on the right) and a fuel pump replay open (on the left).

If you decide to resolder, be sure to use electronics solder, available at many suppliers, such as Radio Shack. You can use a soldering iron (25 Watts, or so) on the smaller connections and a soldering gun (150-300 Watts) on the larger connections. A gun will pump lotsa heat into the PCB quickly, so practice, skill, experience are very helpful.