I use gorilla brand super glue
As soon as the point breaks I usually look at it and the flake and just get a quick assessment of why it broke. Then ask myself why I did that and tell myself, "don't do that again dummy" or something like that all while reaching for the glue.
I make sure the glue surfaces don't have any dust or tiny slivers on them, then run a bead of glue all across the break. I want enough glue to get a little bit of squeeze out all along the break, then put them together and apply some pressure. Not too much but enough to smash the glue out, and I'll lightly try to wiggle them a bit to make sure the pieces are seated together perfectly, then hold the pressure for four or five seconds. Sometimes they are stuck, but sometimes they need a few more seconds of pressure to hold together. Once it's stuck I gently lay it somewhere where there are no bending stresses on the glue joint and let it cure. I think it takes a while to cure because the squeezed out glue is thick enough to take a while to cure and any glue in the joints is kind of sealed in, like glue in a bottle, until the whole mass of glue is cured.
Here's some new action on the point that just keeps breaking
I got the second notch done with no problems at all
I had all kind of trouble with the little narrow section between the breaks in the middle. The edge crushed and took out a little chunk of it. Got worked down to a point that I thought I was fixin to get it and had one short section to run some flakes on when I noticed a crack extending from the edge to one of the glue lines.
You can see the crack in the third pic.
I got two small flakes working my way toward the crack, then it snapped on the third one.
It's interesting how this crack went right through one of the glue joints.
That makes six times I broke this thing. That ought to be enough, but I have it glued and curing again so who knows,