heres a spring loaded tap holder i made for use in lathe for handtapping.
centre section is made from pce of 25mm rd stock i drilled through with 15mm drill, then ran 19mm drill through stopping 10mm from end.
then using some 20mm rd i stepped it down to 18.5mm at end to length of 10mm to act as stop inside tube.
next sect i turned down to 14.5mm x 45mm long to slide freely through end of tube.
last sect i turned to 12mm x25mm long to fit drill chuck on lathe.
finally i assembled it keeping tap holder in place by means of m8 bolt.
using spring means it keeps light pressure on tap.