I’d imagine any old multi grade motor oil would work or good old fashioned 30wt. Machine gear oil is a bit thicker and heavier than 30wt.
The leak is most likely caused by too much oil flowing onto rail face and the top guide shoe is acting like a squeegee. Look at the oil cans afixed to the top of the rails and all tubing to ascertain they’re all in good order.
The tighter the wicking clamps, the less oil will pass through. Once you fill those cans, you’ll want to check back soon and they may need more or less pressure to regulate the flow.
Is it the left side of the ceiling that’s got the leak? If so, lightly snug up the wicking clamp for that side, then clean up the mess and watch.