This hole will recieve the extra piece of 1/3" cold rolled steel. It has now become a mandrel for the handle to mount on the lathe. In case I have drilled slightly off center or at a bit of an angle, the mandrel will force the handle to be concentric to the later mounted tool holder. The hole is 1 1/8" deep but the mandrel is 1 1/2" long thus leaving 3/8" to be gripped.
The handle gets mounted with a Jacob's chuck holding the mandrel and the tailstock brought up for support. Make sure the Jacob's chuck is holding the piece firmly before the tail certer is used.
Turn the handle to a comfortable fit. Normally I like unfinished tool handles but this being a present, I used some turner's polish to finish it.
Remove the hande from the lathe and take the mandrel from the handle.
Use some superglue on the tool holder and press it into the handle.
I then held the tool handle with the tool holder installed in a cradle for the drill press and drilled a hole for a set screw though the handle and in one side of the tool holder. It was tapped for a 6mm x 1 setscrew. A 1/4" x 20tpi setscrew will work as well but I bought a box of 6mm x 1 about 15 years ago and I am still using them. In my case a hundred set screws goes a long way.