Chances are the issue is with the horn relay and not the horn itself.
First off, do you have a battery installed? (not sure how familiar you are with the horns, but on NW2s they require a "C" battery to work.
If the battery is installed, the horn should sound if you turn the switcher upside down, otherwise there is a problem.
if it doesn't sound when turned upside down, check the relay. It's screwed to the horn assembly. take a small screwdriver or something of that sort and push the contacts on the side of the relay together. If it still doesn't sound, then an issue definitely exists, but it might still be in the relay. The contacts might be dirty, or the relay damaged internally.
You can bypass the relay completely. Without looking at the diagram, I believe the process is to run a jumper from the negative on the battery to the horn case, and the single wire coming from the horn to the positive. This I am not certain about, but it is either that, or the reverse. The horn should sound. This would indicate the horn is fine and the relay requires repair/replacement.
If that doesn't work, there are replacements on eBay that range from $20-50 depending on whether the relay is included, whether it is repro or old stock, etc.