What you're describing sounds like a Soviet ШР or РС series circular connector. The notched bayonet collar and the brownish insulator faceplate are dead giveaways for the old Soviet stuff, and the little stamped numbers next to the pins are just standard pin numbering, same idea as the American connectors they were based on. The РС series came later and was basically a knock of the American AN-type circular connectors, while ШР is the earlier cruder generation. Both turn up constantly on Soviet test gear, lab supplies, and military surplus from the 50s thru the 80s.
The reason your searches are going nowhere is that you need the Cyrillic terms. Try 'разъём ШР' or 'разъём 2РМ' plus the pin count and shell size. There are catalogs in Russian that list every variant, and once you have the exact designation like ШР16 or 2РМ24, finding a mating half on eBay or a surplus dealer becomes much easier. The 2РМ series is still produced by a few Eastern European factories, so new-old-stock and even fresh plugs are out there for reasonable money.
One practical note from my own expirience restoring Soviet gear: the Soviet shell sizes don't map neatly onto American sizes, so an off-the-shelf US military connector usually won't mate even though it looks close. Don't force it, the keyway notch position differs. The two realistic options are finding the matching Soviet plug or doing what most of us do, which is cutting off the factory connector and soldering on a modern D-sub or circular plug, keeping the old one bagged with the instrument for originality. Also, if there's any chance of identifying the instrument itself, the model name usually printed on the front panel or a rating plate will narrow down which connector family it uses, since factory docs often list the plug type. A model number plus the Cyrillic connector designation in the same search usually gets you a manual PDF with the pinout, which solves the whole problem.