1996 Ford Bronco Won't Start or Run

Hello davemint,
The fuel pump will need to be checked
The most reason for why a fuel pump fails is debris in the fuel tank.
When replacing fuel pump, make sure the tank is clean by shaking it with the last drop of fuel until it comes out clean . Otherwise installing a new fuel pump in a tank with accumulated debris that killed the first pump will probably kill the second new one within few months.
Your question was about how you can tell if it is fuel pump or the relay.
The best way to check the relay is to shake it.if you hear lite rattling noise,the relay is bad.if you are not sure about the noise, just replace it with the new one.
The Relay - Fuel Pump is located:
Under hood, driver side, front side of shock tower, mounted on relay block .
No buzzing noise does not mean the fuel pump is dead.
If there is power at the wiring harness connector and the pump does not buzz, the pump must be replaced, make sure the tank is clean.

if there is no power at the pump and the relay appear to be good,the wire must be open between the relay and fuel pump connector.