Variable Brush Timing isn't just for big motors. My little power drill's brush assembly rotates to allow the motor to run in reverse. If you want to see a big spark, you can spin the drill up to full speed and then reverse the direction. The brushes are obviously unhappy about being asked to pass current so far from the neutral point on the commutator. You have to release the trigger while reversing due to a wisely placed interlock.
I believe this motor is a universal motor, a cousin of the series wound dc motor often found in electric cars. I don't recall noticing contacts in the brush timing mechanism to reverse the field windings, but I can only assume they are there as it's not possible to reverse the motor without re-arranging the field-armature circuit.
There isn't actually anything wrong with the motor in this drill, the Jacobs chuck has failed. The chuck consisted of a metal mechanism covered by a plastic sleeve. The plastic wasn't securely keyed to the metal and one day it started to turn without tightening the chuck. Without the plastic sleeve, the chuck is much harder to use. I may be shopping for a new drill or working out how to replace the chuck, it hasn't yet succumbed to Jacob's instructions.