What horn is it? Stock? Check the wiring scheme in the Owner's Manual. Wiring differed for various markets (area code!). If the wiring is like Calj suggests, his test is easy to do. If you have a horn like mine, you'll need a relay for sure. Without it the switch will be gone soon.
it started out where I just had to keep tapping the button hard and repeatedly to get it to fire, but now it just died. After disconnecting the horn my multimeter only gets a very weak .50 reading when I press the button, could this be a switch issue?
My assumption is that a switch either works 100% or not at all.
Not quite, if the switch isn't up to it and develops burns, it will build more and more resistance. I'd say in your case it looks like that. But corrosion can also cause it.
If you read 15 V, it
could be overcharging but not necessarily. Some DMMs give funny readings. BTW, you
did select the right range, didn't you? An analogue voltmeter can give a better result. According to the CB500-CB550 Shop Manual (p.94) max voltage is 14,5.
That's a nice bike in the pic.