Nikcole Mini Systems do some very nice parting and grooving tools the indexable carbide tips are as thin as 0.7mm and can be obtained for right hand or left hand holders. The actual tips can cut a flat bottomed groove or can cut minutely tapered so the pip can be on the part held in the chuck or on the piece parted off.

I am very impressed by them and I use the 8mm square holder on my Cowells lathe. I have the next size up holder for use on Myford.

The traditional way to grind a parting tool, either made from square HSS tool bit stock, or a HSS parting tool blade is to grind the tip of the tool to a slight angle, so that the “pip” is left on the bar stock in the chuck, rather than on the workpiece being parted off.

The slight angle can be 10-15 degrees on a short stumpy parting tool, but on the blade-type don’t go more than about 5 degrees or the angle can deflect the blade sideways, resulting in the parted off face on the workpiece being concave.