Fuel pump and relay testing

If it does not run after the fuel is put in and it starts up the pump is bad. The easy way to tell is because on that vintage the relay is only used to turn the pump on to prime the system. The actual power for the pump comes through the oil pressure sender.
As soon as it starts up the oil pressure should jump up enough that the oil light goes out and the pump will come on.
As yours is not doing that you either have a bad pump or there is no power on the gray line. To see if you have power is easy. The orange wire at the relay is battery voltage from a fusible link. If you have power there, jumper from there to the gray wire out of the relay, that goes to the pump.

When you install the new pump be sure to replace the pump power connector if they include one with the pump. They like to get hot and the connection fails because the internal connectors lose their tension when they heat up.

Let us know what you find.