It sounds like you have excessive internal clearances in either the main bearings, rod bearings or oil pump, probably due to wear/metal to metal contact. The reason the light is flickering is because there is a "threshold" at which point the sender tells the light to come on (lets say 5 lbs) and if the pressure goes under that threshold for a moment, the light will briefly flash. As soon as the pressure goes up, even slightly, the light will go out. At idle, the engine RPM is changing slightly on a continual basis, hence the flickering. The faster the engine revs, the faster the oil pump turns, and the more oil pressure you get. That is why when you put the car in neutral, the flickering stops. The car's RPM goes up and you have more oil pressure.
Also, the engine temperature confirms the loose clearance theory. As the oil heats up, it thins, and excessive clearance allows the oil to "bleed" fasters, thus lowering your oil pressure. That's why this only happens when the engine is warm.
There are two fixes, and both are band-aids. The first is to turn up the idle so the light stays off. The second is to add STP or run 50 wt oil. Both will only work for a short time because whatever caused the excessive clearances is not going to stop, and the problem is only going to get worse. Best case you will need a new oil pump, worst case, new bearing/crank/etc.
I rebuilt race engines for a living for 15 years. I've seen this MANY times. Sorry to give you bad news.