Get someone to hold the horn button down and measure both terminals on the horn to ground. One SHOULD show battery voltage and the other SHOULD show zero volts when the horn button is pressed. This is not how I understand your statement above "Pushing horn button applies 6v across the 2 wires".
An easier way to do that is to just short the terminal that's not hot to ground (bypassing the horn button and the need for a second person.) If the horn works then, the problem is likely at the horn button.
