Height gauge addition.

[Toolmaker51]

A solid cone isn't bad as a center finder, but they don't have much 'feel' to ascertain contact with 100% of a hole in both axes. Mitutoyo's [and likely copies] is a pivoting flat arrow on a back plate, and scriber sized arm for height gauge. A fine lever-arm marks the arrow center, indicating a central location to corresponding line on back plate. Best feature is that precise vertical center isn't crucial, but works best on un-chamfered bores.
It's not a scriber, only used to interpret relative position from a reference you establish. Simple as scribing line known height above surface plate, and positioning arrow at the line. A drill bushing atop a 1-2-3 block works for higher precision, from easily calculated center.

It was designed and patented by a resident of Long Beach, Ca.
https://www.google.com/search?q=mitu...aDn7A-z8lZuqM: