Bad switch or connector.
There would be valve train noise if oil pressure was low.
2.3l oil pressure switch should be above oil filter, drivers side rear close to head
If you pull off the connector and Ground that wire, then turn on the key the oil gauge should show 1/3, what you said was normal.
That means wire and gauge are OK, problem is the switch or the connection to the switch.
The oil pressure switch is just a Ground for the gauge, when pressure is above 6psi switch closes and Grounds the gauge to the engine, so only 1 wire is needed.
Because switch is a Ground leave some bare threads at the bottom when installing a new one, it is OK to use sealer, just leave a few bare threads for good ground