Engine Mechanical problem
1996 Chevy S-10 4 cyl Two Wheel Drive Automatic 80987 miles
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What would cause the fuel pump to run constantly with the key off and the relays under the hood diconnected?

Sounds like the oil pressure switch is stuck on. The relay doesn't power the pump full time. The relay and computer power the pump for a few seconds just to build pressure in the system. Once the engine starts it builds oil pressure and that activates a pressure switch. That switch actually powers the pump. It also acts as a safety. No oil pressure and the engine won't run.