Like they have said, if you unplug the horn relay and no more click, then it is getting grounded by the black wire. If you have no black wire then the relay won't click. It is supposed to run from the relay to the half-moon connector in your 4th and 5th pictures which is the turn signal connector. From there it runs up into the steering column to the horn button switch in the column.
There are no wires that run from the windshield wiper motor to the headlight
switch. You should have a yellow a black a light blue and a dark blue wires on the motor and the yellow wire goes to the fuse panel and the rest go to the wiper switch.
Here is a diagram of the underdash truck wiring. It shows the wiper motor connections in the upper left. There is a mistake in the yellow and black wire connection on the diagram. Yellow is hot and black is ground and it should go the washer motor connection.
If you follow the wiper motor wires in the first and second diagrams you can see that they yellow goes to the fuse panel and the rest go to the wiper switch in the second diagram.
Ignore the black arrows and the blue arrow. They are for another problem.
If you look at the left middle of the first diagram you can spot the red green and black wires going to the horn relay. Follow the black wire and it goes over and up to the half moon connector for the turn signal connector.
