The oil pressure light may come on at low RPM idle on hot days or after cruising down the freeway at speed and hitting a stop light following an off ramp when the oil is hot (thin). These two cases are fairly normal occurences for stock engines.
However, it is not normal for built engines which usually have higher capacity oil pumps (30mm gears as opposed to stock 26mm gears).
In any case the warning light should go off immediately off-idle, not at over 2,000 RPM.
You may have a bad oil pressure sender; you can buy a new VDO combo sender that has two outputs, one for a gauge (marked G) and the other for the idiot light, and install it to see if your problem goes away. If not, I would remove and check the oil pump for wear on gear end clearance (to the cover) and clearance between gear teeth and the pump casing (specs in the Bentley manual, smaller clearances are better than larger). Other things to check are oil relief valve sticking open (the one next to the flywheel) and the oil pickup tube being loose in the case.
Note that if the engine case has been full-flowed the oil pump outlet hole in the case should also have been plugged - when it is not, some of the oil in the main oil gallery that feeds the crank bearings may bleed off back into the sump; at low RPM this could create a pressure drop that causes the warning light to come on.
To check the pickup tube for looseness, remove the sump bottom plate (necessitates an oil change) and gently try to wiggle the pickup tube around - it should be a tight fit in the case.
The "quick, tight turns" situation is usually solved by adding an aftermarket bolt on sump that increases oil capacity and keeps oil near the pickup tube during cornering.
If none of this seems to solve your problem you may have a porous case casting (oil pressure bleeding off through the casting wall) or main/rod bearing and/or crankshaft issues.
Good luck...