Another what is it?

[k9gl]

This looks like a handle for holding taps, but there is a problem.  The thumb screws do not have thread going all the way, so they do not tighten close together.  About the best you can do is 1/8" gap, but you are only holding by a thread or so.  No markings, but appears well made.  All steel.

[Bill Houghton]

Looks like a tap handle to me, too, although most of those I've seen have v-notches rather than the rounded grooves you've got.  I'm a touch confused by your confusion; it looks to me like the tool is closing down enough for at least some sizes of taps.

[Aunt Phil]

Cheap tap wrench

[oldgoaly]

may not have been finished?  a square file and some time will take care of that.
unless it is to hold something small and rounded, sure does look like a tap holder.

[leg17]

Shop made for a particular application needing the round shape.
Modeled after tap wrench.

[Chillylulu]

Part of a drafting set....

Chilly

[k9gl]

Looks like a tap handle to me, too, although most of those I've seen have v-notches rather than the rounded grooves you've got.  I'm a touch confused by your confusion; it looks to me like the tool is closing down enough for at least some sizes of taps.

If you look at the threads, they are missing up on the thumbscrews.  If you tighten them all the way, it runs out of thread before the tool becomes tight, and they just spin.  If you leave about 1/8" gap you can tighten on to something, but there is not much thread holding it.  If you have it spaced about 1/2" apart, the thread of the thumbscrew is fully engaged, so it appears to have been designed for this distance.

I tried them with a larger tap, and they do work, but the rounded portion does not match up very well with the tap.  This does not appear hand made either, as the thumbscrews are very nice.

[oldgoaly]

I was wishing I had that! lucky the clog was just lead, I'm cleaning a desoldering head.