I agree with Bubba, and would start by unplugging the wires to the O2 sensor heater (also fed by fuse #4).
Look for a flat, 2-wire plug on the passenger side of the fire wall, with wires feeding into a sheath that also carries the O2 sensor signal wire, and goes down and under the car.

The 2 wire colors are Black and Yellow-Red.

EDIT:
Of the two relays under the white cover, only 1 (Fuel) is for the pumps and O2 sensor heater. The other one is the "Main" FI System relay. It should be energized whenever the Key is on, and powers the ECU, AMM, Injectors, Idle Air Valve, AND the Fuel relay (all with voltage from fuse #6).

The ECU then controls the Fuel relay by its ground side — briefly when the key is turned on (as you saw), but more importantly when it gets timing pulses from the Ignition CU. (No Spark = No Fuel)


--
Bruce Young
'93 940-NA (current), 240s (one V8), 140s, 122s, since '63.

Here is what the 92 manual says about the fuses:

#4 Fuel feed (in-tank) pump, Lambda-sond heating element 8 A
#6 Main fuel pump relay, Lambda-sond, Fuel injection system 16 A

So one of these items is drawing too much current becuse the item is defective or an exposed wire (bad insolation) is touching something it shouldn't. Inspect your wires and maybe try disconnecting the O2 sensor and in-tank pump one at time to isolate the problem.