The wiper motor uses a component earth i.e. the body of the motor being bolted to the car. The secondary earth that runs through the switch is used for the intermittent wiper operation (inside the switch) and also to turn the washer pump on and off. If the fuse blows with the washer pump, wiper motors (both front and rear) and switch disconnected then it indicates there is a short to ground in the wire harness.
I've no wiper/washer circuit diagram for a Starlet, so can only go by my own conjecture. I'll take a huge guess and suggest the 12v feed to the rear wiper is switched, so the 12v feed from the wiper fuse will split 3 ways, to the washer pump connector, to the switch on the steering column and straight to the front wiper motor connector. To confirm there is a short in this circuit, you'll need to use a multimeter set to the 200Ω range and check the resistance/continuity between the circuit side of the fuse and a good body ground point (do this with above connectors disconnected). There should be infinite resistance or no continuity (whichever way you want to look at it). If the meter shows a resistance reading of 0Ω or more then you have confirmed there is a short to ground in that circuit.
Ultimately that means there will be a wire in that circuit that is touching a metal part of the car somewhere. It could be crushed behind a bolt or bracket or possibly have a screw wound through it. Either way it's going to require a visual inspection to find the cause of the fault and might not necessarily be obvious or easy to identify.