Can you give me engine size?
One more quick question- When you turn the key off, does the needle move back down?
Ok. It sounds like you are going to have a faulty Oil Pressure Sensor. This sensor reports to the instrument panel as soon as electricity is given to it, doesn't matter if the engine is running or not. I believe replacing this sensor should solve the problem.
can you give me a part number?
Hmmm... for some reason, i do not get an OEM part number listing... that's odd. At any rate, it's actually a pretty common fail item on the 4.0 (i actually just did one about 2 weeks ago) and is readily available at any local parts store. I had NAPA deliver mine, it was in stock.