As boscoe pointed out, the pump will not always turn on when you turn key on. If when turning ON key the main tank oil sensor detect that the oil level is below the bottom level line, then the pump will turn on.
You've got a brand new pump so no need to test its function. The problem lies with either the main tank sensors or conductivity within the automatic oil system. Remove enough oil from main tank so the level is below the bottom level line. Turn ignition key ON. Alarm should immediately sound but will turn off after the oil pump transfers enough oil into main tank, above the lower level line. If the alarm continues to sound even after oil is above the lower level line...bad sensor. If when turning key ON there is no alarm and no oil transfer...conductivity problem, most likely the oil harness. And if it is, there is no replacing a single wire within the harness. You've got to replace the entire harness.
