Where I tried to write 'camera', you can see a mistake I make frequently, lol. I'm often thinking of the next word/letter before I'm finished writing the first one, so I totally skipped the R at first, lol.
If you have a flash with a bound card, that might put enough light onto the background. A second flash would probably be ideal though.
As long as the flash is not actually in the field of view of the camera, I think you can avoid the massive blown out area overread was talking about.
Or you could do what I think he was suggesting, which is place a bounce card beneath the oil, and aim the flash at that.