1996 Ford Thunderbird Low oil pressure after warms up

I just purchased a 1996 Thunderbird with 149000 miles on it. It runs and drives great so far. I don't expect a 14 year old car to be perfect but this problem worries me. After driving it for awhile and getting it warmed up, my oil pressure gauge will either have no reading at all or franticly bounce from High to Low while idling. It reads fine after initial start up and while driving. If I'm stopped at a light and keep the RPM's above 1000, I will get a normal pressure reading. If I let it idle on its own, it will idle fine with an occasional sputter as if it wants to die. When I get where I'm going and put it in park, the gauge does the same thing but it will idle just fine. My first thought is the oil pressure switch but I wanted to see if anyone had a better idea before I start playing hit and miss. Thanks!