Hi,
I had similar problems once. I have a 63 c10, and for the longest time, the horn wouldn't blow, but the relay would "click." So, i had some help and asked my kid to honk the horn and i was in the engine compartment and jiggled the wire connector that connects to the metal tab on the horn. Found out if i hold it to one side, a nice ringing horn, hold it to the other side, nothing but a positional click.
I took off the connector and "sprung" it, so it would connect to the metal tab nicely and secure. The horn has worked nice ever since.
Moral: Check grounds and all connections first, it's usually something simple. I had thought it was the button multiple times originally and bought 3 types and afterward went back to the original and still is fine.
Also, check your relay for faultiness.
Hope this helps.