I have a 1995 Mazda 121 and I have recently had trouble with the oil light flickering then staying on. I have oil in the engine and have recently changed that oil. I also get a " whirring" noise in my engione when it starts :
You need to find out if your engine is producing oil pressure, or if it is an indication problem. You can remove the pressure indicator sendor and install a direct reading gauge to see if you have oil pressure. Should have atleast 15-20 psi at idle even when the engine is warm. When it first starts, it should be around 40 psi, and as it warms up it will go lower. But never below 15 psi at idle, and should be around 40 psi with the engine rev'd up.
If you do see this pressure when you start, shut it off fast, and repair your oil pump. You can destroy the engine by running with low oil pressure.
If your oil pressure is fine, then you have an indication problem with probably a loose wire or bad connection.