Those that have replied to my ‘what is this’ are on the right track. It is a Coventry diehead, but adapted for cutting long and/or steep tapered threads.
According to my manual standard Coventry dieheads can be used to cut short tapered threads such as NPT and BSPT with special tapered dies that cut along their whole length. In much the same way as one can buy tapered taps and dies for NPT and BSPT.
For longer/steeper threads one needs a diehead that opens up as the thread is cut. That is exactly what the unit shown does. The spigot protruding from the slot at right lower front opens the diehead via a rack as it is pushed back by a stop on the machine tool. The rate of opening is set by an adjustable slide within the unit. The unit is not homebrew, it appears in my edition of the Coventry diehead manual.

I don’t have any Coventry dies for tapered threads. I have never used this unit and doubt I ever will. It was bought out of idle curiosity; can’t remember what it cost but wasn’t expensive.
Julie