Probably the oil pressure sending unit. But you should go rent yourself a mechanical gauge, take off the sending unit and attach the gauge hose there, then verify the actual oil pressure at idle and higher rpm. If the pressure IS excessively high at higher rpm it could be a spun bearing or other restriction in one of the oil passages - bad news. It could also be a filter problem - when did you laast change the oil and filter? The other possiblity is a stuck pressure relief valve that at the low volume seen at idle doesn't cause an issue, but at higher rpm pump output causes enough restriction to raise the pressure. Excessive pressure can cause it's own problems.
The oil pump itself is not a concern here. It is apparently doing it's job.
One other thing to check is for a loose connection at the sending unit or else where in the harness. I've seen this many times on the line of vehicles I work on. At higher rpm the engine vibration/harmonics is just right to cause the loose connction at the sending unit to make almost no contact. On sending units, typically high electrical resistance gives a higher reading on the gauge, low resistance gives a low or zero reading on the gauge.