Similar on mine M3W:
When I switch on the hazard warning lights with the ignition switched OFF, the engine oil pressure warning light illuminates steady and the hazard warning light twinkles. (separate lamps)
With the ignition switched ON the engine oil pressure warning also illuminates steady.
(warning hazard on or off)
I have not tested with the engine running, but I suppose the engine oil pressure warning light is turned off...
(to late hour to wake up everybody!)