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I believe your problem to be the load reduction relay J59 which is located on the relay panel position number two. Both the headlights and the wipers get power from this relay. I would replace the relay to start.
The only other thing that I can think of, is that there may be a problem with the igntion switch, I would suggest you check the wiring and make sure it is sending out power on both circuits. The switch is a two part and has two wires that supply power to several different circuits, if one side is faulty it can cause issues like this. You can also try and wiggle the swich to see if the wipers come back on