Irradic reading at oil pressure guage

do tell what is reading that.>
an hand held guage?
what, name the what.
(some factory guages are NOT RETURN TO zero , when dead)
lots, even fuel guages and others, for 100 years.

Oil sending unit is bad. usually by the oil filter.

Very first thing you need to do is install a mechanical pressure gauge on there to verify what you see on your gauge. If the actual pressure is low, then it's time to start looking inside the engine. If not, then you need to trace out the electrical problem but will know the engine is safe.

First off I wouldnt drive your car until you make sure that you have indeed oil pressure and that the gauge is a false reading, driving your car if in fact it has no oil pressure will severly damage your engine, but firstly i would check the oil pressure switch its located on the passenger side of the engine right back from the oil filter make sure the connector is clean and free from oil and corrosion if the connector appears to be in good shape take a paper clip and insert it between the 2 terminals inside the connector your oil pressure gauge should peak at 80 PSI that tells you that your gauge and all related wiring are good and in working condition, secondly remove the oil pressure switch and hook an manual oil pressure gauge up to you engine and start the engine the guage should have a oil pressure reading anywhere from 30 PSI to 55PSI depending on engine temperature if theres oil pressure on your manual gauge replace the oil pressure switch with a new unit, if you still have 0 PSI on your gauge then stop your engine immediatly and start looking at your oil pump and lubricating system for a problem.

This is a safety system built into a Grand cherokee. If it gets hot or loses oil pressure it will shut itself down to prevent engine damage. If it hasn't been started and it reads hot I would say your coolant temperature sensor for the gauge has gone bad and needs to be replaced. They are fairly inexpensive and not to hard to replace.

First thing you should do is put a mechanical gauge (the factory one in the vehicle is electro-mechanical) on the engine for testing. If it reads the same as the one in the vehicle you either have a blocked pump pickup in the pan or one or more crank bearings are worn out of clearance.
If the mechanical gauge reads normal pressure, replace the sending unit. If you don't have a mechanical gauge available you could replace the sending unit and if it does not help, then you can assume either a blockage or wear is the cause.

When the pressure reads low, are you hearing any knocking or tapping noises from the engine? If so, you may have worn engine bearings. I'd check the actual pressure by having a mechanical gauge installed on it in order to determine the actual pressure (your gauge is electro-mechanical and not quite as accurate) If pressure is actually that low the oil pan must be removed and bearings, oil screen etc need to be checked.
The reason pressure is always higher at first is that when cold the oil itself is thicker...as it gets hot and thins out pressure will drop somewhat, but should not go that low. Only other thing that can affect pressure in that way would be either a bad sending unit (you will know that after testing) or gasoline contamination in oil (happens if an injector is not working properly)
Good luck with it!

Try replacing the oil pressure sending unit.

Just got word from an expert standing behind me (my son); remove the oil pressure sensor (on an I6) near the oil filter, clean it (small orifice) and put it back in. They just 'cured' one this AM.
If it doesn't work, (does 2 of 3 times) it is not an expensive part and widely available. 

if the engine is running normal and there are no odd sounds from engine. probably needs oil pressure switch or bad connection at switch. any ticking noises and i would have pressure checked with guage