In close to 60 years of working on engines, I think I've seen a grand total of three oil pump failures. Two were sheared-off drive tangs from debris getting stuck between the gears, and one was a piece of trash stuck in the relief valve, jamming it wide open. The pump was still moving oil, but it was being recycled right back into the oil pan. Your situation is likely something similar, a sticky relief valve. Drop the oil pan and the pump, and inspect it carefully for wear. Remove the relief valve spring and plunger, and look for burrs on the plunger and/or score marks in its bore. If you see anything suspicious, change the pump. Also inspect the pump pickup strainer screen for obstructions, sludge, etc., or a loose tubing fitting where the pickup line enters the pump.

While you've got the pan off, inspect all the rod and main bearings, and check the oil clearance with Plastigauge. About .0015" is ideal, and .003" is max.
Jerry

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