Fuel Pump Relay Missing?
 

Ok so first off thanks in advance for any help with this. I got a 1992 Chevy S10 Blazer Sport 4.3 v6 vin code z from a lady i worked with for $1(score), it was sitting for about a year before my father in law and me towed it home. She told me that the fuel pump was bad and needed to be replaced. I put in a battery and it started up after cranking for about 5 seconds and i drove it around for about 15 minutes, would the car start if the fuel pump was bad? Also I'm trying to go about this repair from least time consuming to most, so i began with trying to find the fuel pump relay, from what i have read i should have two relays on the firewall, i only have one on the right side, the left is empty and has no wires going up to it, only the one on the right. So is there any reason the truck would start once and not again, with what looks like to be a missing relay?

If im not mistaken,the one on the left is the ac relay. So, yea. If it runs,and drives fine. id say pumps fine and you scored.