Only three leads? A single or two speed motor?
The two-speed wiper motors that I am familiar with use a cam-driven switch behind the big internal gear. When you shut the wipers off, as the motor comes around, the switch grounds out the windings in the motor. If the dash switch isn't doing the right stuff (and it's fairly complex), you could end up with a dead short.
Unfortunately I know nothing of the one-speed motors, although I might have an early MG manual somewhere around.
