Here is a snap of where the stain stands after my first attempt to get rid of it.
Do you guys see the dark patch next to the middle button in the attached image?
If the oil has not yet gummed / resinified, you may want to try out diatomaceous earth. I don't know how it is called where you are located - where I am I can buy it in the pharmacy. It works by absorbing the oil (or other liquids) because it is a powder composed of very small particles that create a huge surface area. This has strong absorbing properties and effectively sucks oil out of fabric. It was even possible once to clean a wood table stained with wax from a candle by using a flat iron to melt the wax first.
To remove an oil stain, I simply sprinkle some of the power over the stained area and let it rest over night, then shake it off and wash the piece. Btw. the ground breaking discovery of Alfred Nobel was to use this stuff as a stabilizer for creating dynamite, so its quite famous.