pressure is a measure of the resistance to flow,both the oil viscosity and temperature effect that resistance to being pumped under pressure thru bearing clearances
if your oil pressure peaks at less than 60 psi, the first thing Id suggest is checking with a separate oil pressure gauge and sensor because its hardly rare for those sensors, or gauges to be defective.
FLOW IS THE KEY HERE!
if your oil levels low that can also cause the symptoms, so verify oil level in the cars engine, before you go nuts. one simple test is simply to add an additional quart of oil and see if it makes a difference in the oil pressure or where in the rpm range a problem shows up.
now if the oil pump pick up is mounted too close to the oil pan floor it restricts oil flow rates entering the pump and as the rpms increase so does the flow up to the point the oil flow can,t enter the pick-up due to the restricted area between the oil pump pick up and the oil pan floor.
this will produce the exact symptom your describing, and can happen at 20psi, 30psi, 40psi,, depending on the pick-up to oil pan floor clearance or bye-pass spring which may be weak and opening early or clearance between the pick-up and oil pan floor,but its not the only possible cause., and its the source of the myth that high volume oil pumps pump the oil pan dry, because high volume oil pumps sit lower in the pan and if you don,t carefully check oil pump pick-up too oil pan floor clearance theres a good chance swapping to the longer pump restricted oil flow into the pump.
the next thing to do is swap to a thicker viscosity oil (save the old oiil)
and a new name brand oil filter,like WIX or MOBILE 1 or PUREOLATOR because oil filters can be defective or get clogged, if the pressure increases, on both gauges to well over 40 psi, to 60 psi you know the gauge is reading the resistance and its not the oil pumps bye-pass because if thats defective, or the pumps intake pick-up clearance, is restricted, the bye-pass circuit will still open at 40 psi. and the pumps still restricted, if pressure goes up, with the thicker viscosity, and new oil filter theres a good chance its the bearing clearances, or the old oil filter was restricted, if you, now drain the oil and put the old oil back, but keep the new oil filter, and it still has the higher oil pressure it was obviously a restrictive filter. if it returns to the 40 max psi, theres a good chance its a restricted pump inlet or defective bye-pass circuit, or excessive clearances
heres a few related threads to read
viewtopic.php?f=54&t=3536
viewtopic.php?f=54&t=150
viewtopic.php?f=54&t=1800
viewtopic.php?f=54&t=3194&p=9385&hilit=scope+clearance#p9385
BTW
THIS TOOL MAKES CHECKING THE OIL PUMP TO PAN CLEARANCE EASIER, drain your oil , and you can use the flexible scope and look at the oil pump clearance to the oil pan floor, the oil pump pick-up and its brazed joint,the cam, pistons and bore walls etc, thru the oil pan drain hole, or pull a spark plug and inspect the valve or piston condition
http://www.tooltopia.com/provision-pv618.aspx