the switch inside the motor
That's the park switch. After switching the wipers off, it keeps the motor running until the wipers are in the horizontal position. At that point the switch disconnects the the motor but also makes a short over the motor to prevent run out (after spin).
For your understanding; inside the timer relay is a timer unit that sends a pulse to the wiper motor, that makes the motor running until the park switch ends the cyclus. After so many seconds the timer relay sends another pulse to make the motor running, etc, etc, etc.
L = 12V power to the wiper relay
W/B = ground
L/Y to L/Y on the switch activates the washer when you activate the interval function (wipe/wash).
L/O to L/O on the switch is the actual interval function.
L/O = the timer output, goes into the switch, exit the switch as L/R and goes to the wiper motor (low speed).
That's my theory as long as the wiper motor is connected to ground in some way.
Toyota used two systems for wipers.
A. 12V to motor, motor to switch, switch connect motor to ground. Circuit closed.
B. 12V to switch, switch to motor, motor is grounded. Circuit closed.
When Mr. T. changed from one to the other system, the guys who make the diagrams made errors by flipping the way the power runs and that's what you see in your diagram and not in my two diagrams.
Anyway..... use an in line fuse (15Amp or so) for bench testing.
Rudi