The switch side of the fuel pump relay gets hot from the computer relay. The computer ground the order side of the relay at pin 22 to finally turn on the fuel pump. This is really a lot easier to see visually with a wiring diagram..
Here is a VERY generic one:
http://econtent.autozone.com:24991/znetrgs/repair_guide_content/en_us/images//0900c152/80/07/81/c7//large/0900c152800781c7.gif
The circuit you're diagnosing is on the left, right under the alternator box, just under the fuse links.
Keep in mind that both the computer and fuel pump main powers have fuses. Either one could be blown.
So both the computer relay and computer have to be functioning for the fuel pump relay to work. Could be maybe just the computer relay you're hearing?
Quick way to test computer circuit / relay / fuse is to check for spark or power on pin #1 (yellow) at the computer. That would narrow quite a bit down to it only being in the fuel pump circuit, or the computer might not be grounding the relay from pin 22.
Also, see the section in the EEC-IV diagnostics in the technical library regarding grounding the terminal at the test harness for testing the fuel pump circuit. Basically that grounds the relay as it would have from pin 22 on the computer.
Pete