You got NO light when the wire wasn't properly connected to the sensor. ... And I can't reconcile your experience with what I saw.
On the YM240, I drove into a downed tree to pick it up and carry it away. A branch poked the sender wire, tearing it off. The oil pressure warning light came on.
I drove back to the barn with the light on, that was un-nerving even though I knew the cause.
Spliced the wire and the system went back to normal, light on only before the engine fires off and runs up the oil pressure.