My fuse keeps blowing fuel pump

Running a new wire to the fuel pump will not solve this and it is not a proper way to do the repair. Imagine if you had a water pipe in your house feeding the kitchen sink that sprung a leak. Your solution is to run a new pipe to the sink, and to not cut off and plug the leaking pipe. You will still be spraying water everywhere.

With your electrical short, that will still be there unless you cut off the wire that is grounded/pinched/shorted, etc. If you know which wire is grounded and needs to be cut off, you know which wire to fix. Fixing a short is much easier than fishing a new wire throughout the car, and, it is the only acceptable repair in my Automotive Electrical class. That is because most of the time you are going to find the wire has a screw run through it, it was rubbing on the sharp edge of a metal bracket, or the harness fell down onto hot exhaust parts. In all cases, how long will it be before the wires next to it meet the same fate? You could be chasing new symptoms with different blowing fuses for the rest of the life of the car. Instead, when you find the location of the short, you can address the cause before it has time to affect other wires and circuits.

You are correct to ask if other things run on the fuse that is blowing. I am searching for a wiring diagram to know what else is on that circuit, but in the meantime, here is a way to work in the circuit without going broke buying bushel baskets full of fuses. A simple trick to finding a short is to replace the blown fuse with a pair of spade terminals, then use small jumper wires to connect them to a twelve volt light bulb. A brake light bulb works well. When the circuit is live and the short is present, the bulb will be full brightness and hot so be sure it is not laying on the carpet or against a plastic door panel. Now you can unplug electrical connectors and move things around to see what makes the short go away. When it does, the bulb will get dim or go out.

Be aware the fuel pump relay is not going to turn on and stay on just by turning on the ignition switch. It should turn on for one second, then turn off again until you start cranking the engine. At this point, with the short in the circuit, what you can expect to see is the test bulb turns on bright for one second when you turn on the ignition switch, then it will turn off. As soon as you crank the engine, the bulb will turn on again until you stop cranking. Those are the two times the relay gets turned on. It is not practical to have a helper sit there and crank the engine non-stop while you poke around in the circuit. Instead, pop the relay's cover off, install the relay that way, then squeeze the movable contact to energize the circuit. You can place a weight on it or use a rubber band to keep it on. This is the better choice when you do not know anything about the relay or its terminals.

Another way to keep the circuit live is to bypass the relay with a jumper wire, but this is where you do have to know which terminals in the socket to jump together. If you have a relay that looks like one of the three in my first nifty drawing, jump terminals 30 and 87 together, or the two indicated. GM uses a lot of gray 1" cube relays with four terminals as shown in my second drawing. Use a test light or voltmeter to find which one terminal has twelve volts on it all the time. Jump that one to the diagonally-opposite terminal. That will turn the circuit on, then the bulb in place of the fuse will limit current to a safe level.

Alternative 2:

For a different method that is more practical when working in a circuit where the relay is not being turned on for you is you can install a new fuse, then use my light bulb to bypass the relay. This way the circuit will be energized all the time, even with the ignition switch off, and the bulb will limit current to a safe 1 amp. Using the bulb to bypass the relay is my favorite choice because it is faster to bypass the relay without having to get the cover off and you do not need to turn on the ignition switch. Remember to have a good fuse installed. Use the same terminals in the relay's socket that you used with the jumper wire, but this time put the test bulb there instead of the wire.

Now that the test bulb is full brightness, it indicates the circuit is powered up, the short is present, and current is not excessive. A good place to start on GM cars is by moving the rear seat cushion around. On many models, the wiring harness runs under the seat and it can get crushed over time. Brake and tail light wires are in that harness too. Next, look around the exhaust pipes to see if a harness fell down onto hot parts and the insulation melted through. Often the internal heaters in oxygen sensors are turned on at the same time as the fuel pump is running, so they all run on the same relay and fuse. It is possible, although not real common, for the heater in an oxygen sensor to short internally to its ground wire, so unplug each oxygen sensor to see if the short goes away.

For my final great and wondrous words of wisdom, be careful on GM products when poking around in the relay and fuse sockets. Those terminals spread very easily if you stick in a terminal that is fatter than those on the relay or fuse. They are also real easy to damage by poking a voltmeter probe or test light probe in there. When using meter probes, just touch them to the terminals; do not stuff them in all the way. Doing so will spread the terminal, then it will make intermittent contact. We damaged a lot of these on my "bugged" cars, and it takes a lot of time to pull them out to fix them or replace them.