Hard time locating schematics, so I'm going to shoot from the hip ask all your friends and mechanic friends anybody that might be upset with you to end the joke. My friends can be really mean and I've had some pretty funny ones when you put your turn signal on the horn also beats with the turn signal blink.
The wipers work on a multiplex signal line using resistors to cut voltages and doing them in binary signals. Okay let me cut to the chase, the 12-volt signal that is sent to the starter solenoid is somehow bleeding over onto your Multiplex signal line from your switch to the controller. Try disconnecting the switch and starting the vehicle.