I have never had this issue with not starting when checking oil pressure on a 4.0 liter jeep engine....which sounds strange. The service manual states to disconnect connector, remove sending unit, install guage and observe pressure readings. If disconnecting the sending unit makes no difference then I dont believe you need to worry about the sending unit or the oil pressure test. It sounds like its an electrical issue. My feelings are towards the instrument cluster.
I want you to try the cluster self test and pay attention to the oil pressure guage during the self test to see what it does as compared to the other guages.
WARNING: ON VEHICLES EQUIPPED WITH AIRBAGS, DISABLE THE AIRBAG SYSTEM BEFORE ATTEMPTING ANY STEERING WHEEL, STEERING COLUMN, OR INSTRUMENT PANEL COMPONENT DIAGNOSIS OR SERVICE. DISCONNECT AND ISOLATE THE BATTERY NEGATIVE (GROUND) CABLE, THEN WAIT TWO MINUTES FOR THE AIRBAG SYSTEM CAPACITOR TO DISCHARGE BEFORE PERFORMING FURTHER DIAGNOSIS OR SERVICE. THIS IS THE ONLY SURE WAY TO DISABLE THE AIRBAG SYSTEM. FAILURE TO TAKE THE PROPER PRECAUTIONS COULD RESULT IN ACCIDENTAL AIRBAG DEPLOYMENT AND POSSIBLE PERSONAL INJURY.
The instrument cluster actuator test will put the instrument cluster into its self-diagnostic mode. In this mode the instrument cluster can perform a self-diagnostic test that will confirm that the instrument cluster circuitry, the gauges, and the PCI data bus message controlled indicator lamps are capable of operating as designed. During the actuator test the instrument cluster circuitry will sweep each of the gauge needles across the gauge faces, illuminate each of the segments in the Vacuum-Fluorescent Display (VFD), and turn all of the PCI data bus message-controlled lamps on and off.
Successful completion of the actuator test will confirm that the instrument cluster is operational. However, there may still be a problem with the PCI data bus, the Airbag Control Module (ACM), the Body Control Module (BCM), the Controller Anti-lock Brake (CAB), the Sentry Key Immobilizer Module (SKIM), or the inputs to one of these electronic control modules. Use a DRBIII® scan tool to diagnose these components. Refer to the appropriate diagnostic information.
If an individual gauge does not respond properly, or does not respond at all during the actuator test, the instrument cluster should be removed. However, check that the mounting tabs securing the inoperative gauge or gauge set to the instrument cluster electronic circuit board are properly installed and making good contact with the instrument cluster electronic circuit board before considering gauge replacement. If the gauge mounting tabs check OK, replace the faulty gauge or gauge set.
If an individual indicator lamp does not illuminate during the actuator test, the instrument cluster should be removed. However, check that the incandescent lamp bulb is not faulty and that the bulb holder is properly installed on the instrument cluster electronic circuit board before considering instrument cluster housing and circuit board replacement. If the bulb and bulb holder check OK, replace the faulty instrument cluster housing and circuit board unit.
If any or all segments of the VFD fail to illuminate during the actuator test, the VFD or the instrument cluster electronic circuit board is faulty or damaged. The instrument cluster housing and circuit board unit must be replaced.
The instrument cluster will automatically exit the self-diagnostic mode and return to normal operation at the completion of the test, if the ignition switch is turned to the Off position during the test, or if a vehicle speed message indicating that the vehicle is moving is received from the PCM over the PCI data bus during the test.
Begin the test with the ignition switch in the Off position. Depress the odometer/trip odometer switch button. While still holding the odometer/trip odometer switch button depressed, turn the ignition switch to the On position, but do not start the engine. Release the odometer/trip odometer switch button. Monitor the operation of the suspect gauge(s) and/or indicator lamp(s).
Depending on the self test results....you may need to access the PCM to see what the actual oil pressure readings is and compare it to the cluster. If different, then the cluster will need to be replaced.