There's two things that can show you an oil light.
If the pcm gets a signal that the oil pressure is below.. IIRC 5psi
The other would be if the oil level sensor (front of oil pan) is not seeing the level or disconnected.
Very likely the seal in the oil pressure sensor is bad and you need to replace it. However..the ticking leads me to think something else is up. I'd have the warm pressure checked with an actual gauge.