1. Indexing.
A headstoc kdividing attachemnt is a bit up market.
If your lathe is backgeared with 60 teeth, you need only make a lock that engages in the teeth.teh ohter way is to set hte work in a 4 jaw and use each jaw as the reference.
I have a dividing head, so I just bodged up a little platform for hte head, and stuck it into the back of the spindle.
2. Actually chomping.
I just made my cutter the width of the side of the square. Drill such that dia = side. Feed across to a total of 1/2 one side. Index round. The reason for doing all 4 sides is just to get a decent finish.
You could make the cutter 1/2 1 side and do each corner singly, but then the load on hte cutter is assymetric and it is likely to deflect. But you could clean up with a square file.
I have used the 1/2 side method, but only on bigger squares where the tool was rigid enough along its length.