This thing has no markings, except for the number 153 stamped under the cap on the back. It has what appears to be four countersinks and a hole punch, that fit surprisingly tight and secure when inserted into the handle and the thumbscrew tightened only slightly.
I’ve seen drills that were being sold as “medical tools,” eggbeaters and small braces, that have a similar aesthetic. Is it an old surgical countersink? Seems weird, to be working on someone, countersinking a bone, with the other tools that came in this set rattling around in the handle. But bone countersinks do exist.