Goatman's comments are good BUT:
Before you do any of that stuff, take a GOOD look at your oil pressure switch and its
associated wiring. The symptoms you give are those of a shorted wire or a bad switch.
I've had them get against the exhaust pipe and melt the insulation and give a low reading
as you describe. I've also had the wire wear through against rough objects under the
hood.
I have also had oil pressure switches fail in the "lit" position and indicate low oil
pressure when there was really no problem.
I have had lots of them leak oil also, while otherwise functioning normally.
They are cheap and easy to replace, so I would do that FIRST.