Anybody know what a capricious oil light means?

Okay, so it’s not really capricious.
The light seems to behave normally until the car is properly warm (halfway between the C and the H on the thermometer). Once warm, the Check Oil light will go on whenever the motor falls below 800–1000 RPMs (like when you’re idling at a light), and turn off again once you cross that same threshold. For a little while, putting the car in neutral or park had the same effect as revving it up to 1000rpms. Sometimes it’ll turn on, then turn off, then turn on, then… you get the idea when idling the engine.
The oil levels are adequate.