The fuel pump relay will have +12 volts on the one side of its coil as soon as ignition is turned ON.
The other side of the relay coil however will be waiting for the ECU to connect it to Ground so that the relay will energize....this is what you need to look for!
The ECU will provide this Ground signal to the Fuel Relay only when the engine turns over and the ECU starts to recognize the pulses coming from the Crankshaft Sensor.
So you should read +12 volts on pin 86 of the relay with ignition ON...if you ground pin 87 the relay should energize and the fuel pump should run. If this happens then maybe you need a new Crankshaft Sensor!