I did something similar on another bike, installed a LOUD horn but also had to install a relay. Most likely there isn't enough juice to push your new horn. I think there's plenty of info in cyberspace, if you google "installing a horn relay".
One way to tell if you need a relay, hook up the horn to stock leads, which sounds like you have, and it did not work. Then hook up the horn positive directly to the battery, negative to frame. If it sounds, you need a relay.
Lighter than needed wire gage may even allow the horn to work momentarily but create issues when in actual use. A relay is a great way to power the horn using the factory switch to activate the relay and utilize a heavier gage wire to power the horn. Listen to sfair. He's competent.
Again, not necessarily so. What if there is a fault in the horn circuit?
Well that's a good point. If the original horn never worked, could be a cct problem. I had assumed the reason for the question was to just replace the stock horn (working?) with an aftermarket, (louder) horn. That's the reason I replaced mine. It was just too soft to do any good. But to go louder, I needed a relay.
A relay may or may not be required depending on current draw. I would be really surprised if Harley used one.
I can't speak to the stock wiring for Harley compared to these bikes. I've had 3 HD's but never needed to replace an HD horn for a louder one. So I'm not sure it's an apples to apples comparison - using an HD horn on an HD may not need a relay but maybe the same horn on an 800A might need one. I've seen ebay adds for HD horns and they sometimes will say a relay may be needed. Anyone else replace a horn for a louder one? I'm sure I'm not the only one. All I know is my replacement horn did not work until I put in a relay, then voila.