Geo Thomas advised the method many years ago & in his inimitable way, explained the "best" way to do it. (it's on page 291 of the collection of his words of wisdom in "The Model Engineers Workshop Manual" Vol 1 (it'll also be in ME magazine of course). Well worth reading if you're having problems
There's nothing magic about using alum. All it is doing is accelerating corrosion (rusting) of the steel or rather the Fe to be precise. Dilute mineral acids work just as well.
As an expert, with years of experience in breaking drills and taps
in bronzes, there are two major reasons why alum or acid corrosion doesn't appear to be working. The first is because a thread lubricant, other than saliva, was used before breakage. Not surprisingly, this prevents surface action on the broken drill or tap. I've seldom had any success getting rid of such lubricant with broken small drills & taps in situ as the flutes are choked with it. If the part is small enough and you have access to an ultrasonic cleaning bath, this will remove most of the trapped oil & swarf but by Sodde's law, the part with the snapped tap or drill is invariably too big to fit the bath.
The other problem is trapped gas
…….bubbles preventing access of alum soln or acid so these need to regularly dislodged.