I've made a number of successful carb needles by placing the drill rod or music wire needle in the lathe chuck, The Dremel tool with an alum oxide wheel is placed in a holder on the toolpost, and the compound rest of the lathe set to the needed taper angle. My lathe is an old worn out 9" South Bend. I use the compound rest's leadscrew to move the grinding wheel across the needle end (using very fine feeds) until the needle is finished to a fine point and nice smooth finish. Very slow to do, and limited to about 1.5" of taper, but gives a good result. The lathe ways are covered with a cloth during these ops to keep the grinding dust out.