The "gauge" on a Ford hasn't been a real gauge since 1984 when they put in a switch and resistor instead of a sending unit.
The "gauge" needle just reads normal or low, there is no in-between, hence it is really a warning (idiot) light with a needle.
I would install a real oil pressure gauge on any vehicle that just has a switch, as a switch just tells you if it is below a threshold level, not if you have the necessary 10PSI per 1000 RPM to keep from wiping and spinning bearing inserts.
Until then have a shop hook up a diagnostic oil pressure gauge to the port on the engine to see if the pressure really is low or if the switch is just bad.
The wire to the switch could also be loose and is losing contact or might have a bare spot that is grounding out both due to engine vibration. If the needle behaves differently in reverse than in drive or neutral I would suspect a wiring issue.
Also just FYI don't use thicker oil in any engine that is OHC (yes I know the 4.9 and 3.8 both are OHV not OHC) With thicker oil on an OHC engine you may have higher bottom end pressure but could starve the head and cam bearings of oil volume due to the metering orifice in the head oil passage.
over 80000 miles?
try thicker oil maybe 10w40
my Windstar did the same thing.
changed to a 180 degree thermostat.
....165' not availble for my 3.8litre.
more clearly, my engine has 117,00 miles and the bearings are worn,so
oil pressure is low at Low RPM.