Just out of interest, my dad used to use the oil he put in 2 stroke motors, i think it was some sort of synthetic oil and was a deep red colour. He seemed to never have had an issue with stones clogging up. But as long as whatever he was sharpening was good enough for the job in hand he was happy. Would this oil be suitable as non-drying and non-varnishing?
I'd be more concerned about other unknown additives in such oils, like petroleum solvents, detergents, anti-corrosion additives, etc. Sometimes the unknown additives may create health hazards via ingestion, absorption through the skin, or inhalation of vapors, etc. It's possible some of these other oils are safe, but it's harder to know for sure.
Pure, 100% USP-rated mineral oil doesn't have any of those 'unknowns', in terms of other added ingredients with possible serious risks to health. That's what I like about using it, aside from the fact it's also known to work best with oil stones anyway. The USP grades are food-safe, meaning there's no toxicity issues so long as you're not drinking cupfuls of it straight from the bottle or inhaling it. This is the stuff sometimes used as a suspension for medicines, for skin care products, as a laxative, etc. So it has a track record over decades' of time for being safe to use, even when ingested in relatively small amounts. And quality honing oils like Norton's are 100% pure mineral oil and rated food-safe as well. All of this means to say, it's worry-free for a use as basic as lubrication for a sharpening stone. I like 'worry-free', so I can just enjoy the sharpening process.
The 'light' or 'white' mineral oils are usually considered food-safe as well. This includes oils marketed for use with food-processing equipment, for lubricating paper shredders, hair clippers, etc. I've liked some I found at a restaurant supply store for lubricating food-processing equipment. It's clearly marked as food safe and 100% pure, and is a close working match to the more expensive Norton Sharpening Stone Oil, which is my favorite overall. All of these 'light' or 'white' mineral oils are completely colorless, odorless and tasteless as well. Very clean stuff.