The admonition not to use a drill, is because most drills turn CW. Tell some guy it is OK if the drill is reversible, and set to CCW, and Murphy's Law says he will use it in CW mode.
Most failures in the speedo gearbox are due to the internal worm wearing down to nothing.
this is due to lack of decent grease. I grease mine before any long ride , and then probably every month or two
With the gearbox removed from the bike, and with the cable attached to the gearbox, spin the drive dogs with the fingers while holding the end of the speedo cable to offer resistance. If no rotation of cable, the worm is shot.
There was a thread recently on home repair of gearbox posted on this Forum. IMO, a new Smiths is the way to go....avoid the knock-offs.
Slick