ballast does get hot, that's why its ceramic and changes resistance with heat, the hotter it gets the more resistance it creates to reduce the voltage to the coil. A Horn relay is simply an electromagnetic pole tied to a microswitch. the coil of the elctromagnet energizes when you hit the horn and the new magnetised pole pulls the contacts closed to operate the horn. Its a way to allow a very small capacity switch (horn button) to trip a large amp draw device and not melt. If the relay is hot to the touch, you may have a grounded coil inside the relay. They are inexpensive to replace, but you could test with a multimeter the various contacts. one is going the be ground. This one has a buzzer for the seatbelts IIRc. Violet is power in...?
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