Reminds me superficially of a valve seat concentricity gauge.
Long rod (pilot) to fit into the valve guide. The gauge slides down over the pilot. The little arm sets gauge preload, and rides on the valve seat. Spin the gauge 360 degrees on the pilot. If the seat isn't concentric, the little arm pushes the gauge up and down on the valve guide pilot, which results in the gauge needle deflecting.
OTOH, while it's common for concentricity gauges to use a 0-50-0 gauge, they're pretty worthless considering that a valve seat should be within one or two thousandths, not fifty thousandths. A 0-5-0 gauge makes more sense in that application.
I've also not seen a valve seat concentricity gauge that didn't use a standard valve guide pilot. Perhaps something along that line, but for a specialized application???
Or is the smaller-diameter rod with the hole in it installed upside-down? The part that would fit into the valve guide is jammed into the tool, while the through-drilled end should be the "top", with the drilling used for the valve guide pilot installer/remover tool. I lean towards this theory. At any rate, even if the gauge itself is repairable, it's a poor substitute for a 0-5-0 gauge; and the guide pilot is ruined from the rust. They're intended to be a precision-fit in the guide. In shop use, you'd have dozens of pilots to fit the various valve guides--from about 5mm or even smaller, through 3/8" for automotive stuff, and larger still for Diesel engines in trucks or off-road equipment. Each nominal SAE guide size will have perhaps 3 oversizes by .001 to allow for honing/reaming to achieve appropriate valve guide clearance. For example, if servicing a 5/16 valve guide, you'd want a 5/16 pilot, a 5/16 + .001, 5/16 +.002 and 5/16 + .003 pilots. Same for 11/32 valve guides, and 3/8 guides, and all the other sizes. On top of that, it used to be common to ream worn guides by 0.015 for re-use, so now you need the nominal size plus .015, .016, .017, and .018. Then, just to make things even more complex, the TOP of the pilot has to fit the reconditioning equipment. My stuff uses so-called "Sioux" size pilots at 0.385. I think Black and Decker seat grinders use pilots where the main stem is 0.375. Therefore, a concentricity gauge has to be matched to the pilot it's used with. This gauge seems to have a single pilot jammed ***-backwards into it.
I looked around on-line for a suitable photo of a concentricity gauge for valve seats, and didn't see one right away. Mostly, shops are either not checking concentricity (they rely on their expensive seat 'n' guide machine to do the cutting properly) or they've moved away from this style gauge to newer/better/far more expensive tooling.