I tap under power (Admittedly using the "Jog" function of the VFD contyrol box )
A Mandrel Handle comes into it's own on lathes lacking this facility, and allows the operator to be aware of the torque being applied, before the Tap breaks!.
Having used a Tailstock Sliding Die holder, I made up an ER25 collet holder for taps of various sizes.
A ME 40 tpi thread will not withstand trying to pull a heavy Tailstock along the be when the Tap is held in a drill chuck.A sliding Tap holder imposes minimal load on the Tap to move it forward into the work.
Torque reaction is taken by a stud screwed into the body, which rests against the side of the front toolpost.
It has the advantage, that if anything jams, the Tap ,slips in the collet rather than breaking. If it is just things getting tight, the Tap can be left in the work, the tap holder removed and with the Tap, hopefully now correctly aligned, the job can be finished using an ordinary Tap Wrench.
Howard