Magneto Pinion extractor is only of use with the fixed magneto drive gear used with Manual Advance maggys. Sure it is Auto Advance?
If so, a homespun claw type extractor should do the trick, along with gentle heat if required, not the traditional smack with the hammer. Avoid both if you can.
Make the jaws tips not less than an inch apart. This means they they will reach well behind the gear and will act on the central metal boss, and not the fragile fibre gear.
That ATD was supposed to be self extracting, so no official Lucas or BSA tool for the job was ever marketed.
Swarfy.