Hi, I also have this book and I’m currently making the grinding rest described within. I’m not sure about sharpening centre drills, maybe if you had one of the common swing type drill grinding attachments that are also described in Harolds book you could rig it up to hold a centre drill? Remember the projection from the front of the attachment is specific to the diameter of drill being sharpened so this would be the pilot diameter of the centre drill. I’m pretty sure the angle of the pilot tip of a centre drill is 60 degrees aswell as the conical, centre forming section, but I could be wrong…
Also, you can’t shorten the pilot section too much as the length is needed as clearance for the tip of your tailstock centre once an impression has been made with the centre drill.
I broke a centre drill today (whilst making the fence for the grinding rest). The pilot of the centre was well bedded in to the material so I marked out for the hole on the opposite side, centre popped, centre drilled and then very gently drilled until the drill felt as though it wasn’t cutting. I placed the material in the bench vice and centre punched the bottom of this blind hole. This punched the broken section of centre drill out the other side! Beats trying to ‘chisel’ it out with old scribers! Sometimes trying a magnet is useful aswell if it’s not stuck in too tight.