Over the years have made various ntapping aids.
The ones most used are:
The spring loaded centre type, in the Mill
A pillar type tool made from an old drill stand and a piece of box section with two sleeves welded in and reamed afterwards, to carry a spindle with a small drill chuck on the lower ens, and short T bar on the upper.
The box section can be clamped up and down the pillar, and swung around it to align with the work, (Usually held in a cheap drill vice )
At one time such devices were available commercially.
For the lathe, I made up an arbor for the Tailstock, so that a home made ER25 collet holder could slide along it.
This was inspired by a sliding Die holder set up
The holder is slightly loose fit on the arbor, so that the tap can not only slide, but float to ensure that it follows the drilled hole.
Howard