Get a flashlight and shine on the dash and see if someone just put a piece of black electrical tape over where the oil pressure light would be, you won't be able to see the silhouette of where the lights are unless you shine a very bright light on the dash while the car is turned off.

 

Just checked mine and it should come on and stay on with the other lights before ignition

It doesn't go off until you start the car.

 

Ok now I'm confused. I came out to check when i got home. First time i cycled to ignition on engine off i got this

 

Second time forward i got this

 

Apparently it's only coming on every once in a while. Slightly troubling

 

Yeah looks like you have an intermittent failure of the LED light on the dash. I wouldn't worry too much about it, just check your oil level regularly.