When you first posted, I didn't understand what you were talking about with the gearbox..I thought you meant gearbox as in 4 speed and reverse

I worked it out just then...
Well done on spotting it, my guess would have been the switch but you've proven otherwise. Now that it is fixed, the problem is easy to reverse engineer. The wiper motor is supplied with 12 volts, and actually grounded out through the switch when you turn it on. So it sounds as if the wiper motor was shorting down to ground internally, hence it ran until it was bored.
All after the fact of course I've worked it out, but its a tricky one all the same.