I just stumbled upon this video. I didn't make this, but this is exactly what is happening.
http://www.youtube.com/watch?v=UZvwwJ2KgBU

 

I just checked my Dodge Service Manual. Here is what it says about the oil pressure sending unit:

OIL PRESSURE SENSOR/
SWITCH
DESCRIPTION
The 2–wire, electrical/mechanical engine oil pressure
sensor (sending unit) is located in an engine oil
pressure gallery.
OPERATION
The oil pressure sensor uses two circuits. They are:
† A signal to the PCM relating to engine oil pressure
† A sensor ground through the PCM’s sensor
return
The oil pressure sensor returns a voltage signal
back to the PCM relating to engine oil pressure. This
signal is then transferred (bussed) to the instrument
panel on a CCD bus circuit to operate the oil pressure
gauge and the check gauges lamp. Ground for
the sensor is provided by the PCM through a lownoise
sensor return.
REMOVAL
(1) Disconnect the negative cable from the battery.
(2) Raise vehicle on hoist.
(3) Remove front splash shield.
(4) Disconnect oil pressure sender wire (Fig. 107).
(5) Remove the pressure sender (Fig. 107).
INSTALLATION
(1) Install oil pressure sender.
(2) Connect oil pressure sender wire.
(3) Install front splash shield.
(4) Lower vehicle.
(5) Connect the negative battery cable.

And that is all it says about it. It receives a ground input from the PCM and sends a signal relating to the oil pressure back to the PCM, probably a varying amount of a negative ground signal.

Based on the video, and based on the fact that none of the other gauges are acting up and the truck has normal oil level and runs OK, either there is a bad connection at the sensor's wire connector plug or the sensor itself is bad. I bet the sensor is bad. Again, I don't know about a 4.7 but if it were a problem with the PCM it seems to me it would throw a code for it, like one of these:

P0522 Oil Pressure Voltage Too Low Oil pressure sending unit (sensor) voltage input below the
minimum acceptable voltage.
P0523 Oil Pressure Voltage Too High Oil pressure sending unit (sensor) voltage input above the
maximum acceptable voltage.
P0524 Oil Pressure Too Low Engine oil pressure is low. Engine power derated.

Those are from the Dodge Service Manual too. Maybe do the key dance and see if you have either a P0523 or P0522 code stored, but I think you would only have those codes if the sensor was completely dead. I think your sensor has some kind of intermittent problem. I know nothing about a 4.7 but based on what I have read about it in the manual I would say try a new oil pressure sending unit.

Jimmy

 

UPDATE: It took me some time to get to it. Had some bad weather, and I don't have a garage to work in.
ANYWAY, replaced the sending unit and presto! the problem solved. Thanks for the tips and advice everyone!