/// If the fuel pump won't run with the new relay in the problem is the coil control circuit for the relay. Look it up in a circuit diagram for your car. Look at the relay socket and find the relay coil connection, battery side. Test for voltage while cranking, or when the engine stops. If y ou have voltage there the problem is the other side of the coil, ground. Test the other side of the coil connector in the relay socket for ground when the engine is stopped, failed. It will read normally if it did not fail first.

You already checked the fuse for the relay circuit, right. It can't be bad since the pump works when you short the relay switch points. Put your hand over the fuse block after running and clean any others that are hot.

If the radio and wipers work, (the car runs) the ignition switch should not be involved unless you can find that there are two parallel sets of switches in the ignition switch. There should be only one wire, one switch at the run position of the ignition switch.

Find out why you do not have a complete circuit through the relay coil when the car fails. Start as I posted above with the relay socket and ground.