As I have replied to similar questions on Usenet before:

First order of business is to put a mechanical oil pressure gauge on that
engine and confirm if you do or do not have oil pressure.  If you don't have
any oil pressure, or if it is as erratic as it seems it may be,  DO NOT run
the engine anymore until repaired.

Fords "idiot" oil pressure gauges are poor at best, they are dampened so
nobody gets excited about normal pressure fluctuations, and they never show
an actual pressure value.  You can check the throw of the gauge by
unplugging the sending unit, and taking a jumper wire and grounding the lead
that plugs onto the oil pressure sending unit.  With that lead grounded your
gauge should show full/max scale.  If it doesn't work properly I suggest you
consider installing a real oil pressure gauge.

Good Luck