My high school machine shop instructor taught that clock oil, sperm whale oil, or porpoise jaw oil were the only lubricants that should be used on machine-shop measuring instruments such as micrometers, vernier calipers, and dial gages.
A few years later, one of my college instructor told us that he considered mil-spec aircraft instrument oil to be the best instrument oil, but the Starrett oil would do.
Some years later, I came across a NBS (now NIST) publication that specifically states that the NBS used USP mineral oil on their SIP circular dividing engine.
Later still, I was working "in the field" when a very- needed mechanical micrometer was accidentally dropped into a mud puddle.
We had clean water available, but no light oil. I disassembled the micrometer, washed it thoroughly in clean water, and set the pieces on a too-hot-to-touch truck fender to dry. A half hour later, the micrometer parts were hot enough that I needed a rag to pick them up.
The micrometer didn't like being put together dry, and the lightest lubricant on site was Lubriplate #105, a NLGI #0 white calcium grease.
After being lured and reassembled, we field-calibrated it by measuring improvised standards (several different size fooling balls, and some short parallels. The Mike was good enough to use.
It ended up operating more smoothly with the Lubriplate 105 than it did with whatever oil the cal lab used.
For the last several years, I've been using an all-synthetic 0W-20 engine oil on my own micrometers and slide calipers. I tried the engine oil on the suggestion of a former co-worker who has a lubrication engineer in his family.
I'm completely satisfied with the synthetic 0W-20 engine oil, and it's available at gas stations, grocery stores, big-box stores, and auto part stores in every city and most small towns in the country. A quart bottle sells for less than $10 Including tax, which is probably less than a can of Starrett Instrument Oil.