"Wire from the battery to the horn relay" -> According to the Dan Masters diagram, on a 73, the horn relay is supposed to get power all the time, through the "purple" fuse. The horn should only sound when the horn button provides a ground for the relay coil.
I am guessing that you ran your test connection to the output terminal of the relay. The next test would be to try grounding the coil terminal that has the black tracer and see if that makes the horn work. If so, the problem is closer to the horn button. If it doesn't work, check the voltage on the purple terminal while grounding the PB terminal. If you find full battery voltage, the relay is the problem.