Oil pressure gauge jumps around after warmed up Have replaced sending unit and gauge
Replace the sending unit with an oil pressure test gauge to see if the gauge also jumps around.
If it does, try replacing the oil filter. The by-pass valve in the oil filter may be defective.
Tester
For about 30 years Ford oil pressure gauges have been phony. The sender is just an on-off switch that closes at about 12 psi and grounds the sensor circuit through a resistor which keeps the gauge reading about 50%. Of course Tester’s suggestion to test with a mechanical gauge is your best next step and if the pressure is constant and above 45psi cold you need to closely inspect the wiring harness and if no problem is found there the instrument cluster may have a glitch.