I have a Tailstock die holder, so made a tap holder, to use ER collets, to slide on the same arbor. Like the Die Holder, a stud is screwed into the body, to rest against the fourway toolpost, as an anti rotation device.
The slight clearance between Holder and Arbor allows a bit of float to allow alignment.
The grip of the ER collet, even when tightened hard, will still allow the tap to slip if it jams, or bottoms in the hole.
Tempting fate, so far have had no broken taps, even with 3/16 x 40, which was the reason for making it. 40tpi taps will not pull a Tailstock along a lathe bed, (certainly not mine) preferring to strip the thread.
Howard