Pump not working with new relay if I hot wire straight the pump runs. What is wrong?

It sounds like you have done some troubleshooting on your own and have determined that there is a problem with the power wire to the fuel pump. Running a new wire from the fuel pump power wire to the relay is a good solution if the original wire is damaged or burnt out.
Before connecting the new wire to the relay, it is a good idea to test the fuel pump by running a wire from the battery positive terminal to the fuel pump power wire. This will ensure that the fuel pump is working properly.
Once you have confirmed that the fuel pump is working, you can connect the new wire to the relay. It is important to connect the wire to the correct pin on the relay. In this case, you should connect it to pin 87, which is the power output pin.
It is also important to ensure that the wire is properly insulated and secured to prevent any electrical shorts or damage. Once the wire is connected, you can test the fuel pump by turning the key to the "on" position and listening for the fuel pump to engage.
If everything is working properly, the fuel pump should only receive power when the key is turned on, and the new wire to the relay will provide a reliable power source for the fuel pump.

Do you have power at your fuel pump relay?

The PCM - engine computer is not energizing the relay probably . Depends on the make , model an year vehicle .
Fuel Pump Electrical Circuits Description and Operation

I just looked at a wiring diagram of the fuel controls for this model: there is no fuel shut-off switch in the wiring. It's pretty straight forward, typical fuel pump controls: the fuel pump relay is in the under-hood power distribution center. When this relay is turned on, power is sent to the fuel pump, nothing else is in the path of the hot wire to the pump module so it (the pump) should be working.

So if pump is not on, you can diagnose the wiring right here at the fuel pump relay. First you verify the power feed for the pump is available at the relay. (One terminal at the relay will have battery voltage with key off. If you pull the relay out and use a test light, one terminal position will be hot.) Next you verify the relay is working, sending power to the fuel pump in the gas tank. You do this by having someone cycle the key to on, while you hold a finger on the relay (it's back in place) to feel it click on. You should feel it, maybe even hear it, the relay will energize every time the key is turned to on, and this is what sends power to the fuel pump.` If it all works, and the pump is not on, the pump probably needs replacing. If the pump relay is not clicking on, that's a wiring hassle, including the wire to the engine computer. The pcm is what controls the relay turning on.
Do you know if the fuel pump has ever been replaced in the car? If it is original, it has been a good long run.

When you say the fuel pump relay is good did you test for power to the relay circuit ?

You need to replace the fuel filter. Also the age of the car warrants replacing the fuel pump too. If its drawing high amps the relay will fail. Straight wiring a fuel pump is a safety concern. A fire or explosion hazard exist due to arcing at fuel pump motor. Yes it is inside the fuel tank and is very old. Replace it.

Cut-off Switch, Relay wiring, battery cables, wiring

Personally I wouldnt bother tracing the wire as it is probably not worth your time, and just run a constant 12v from the battery to the relay on like 10ga wire. There is probably a short somewhere in the system which can be a real headache to find.

Also it may sound dumb, but check your fuses, and the fusible links under the hood. Chances are that they are all fine though, especially if you have dash lights.

Check the fuel pump relay