I think you are going to have to re-write that a bit to make it clearer

As it reads, the horn switch "works" when "disconnected"

Though I guess you mean you have tested it with a multimeter whilst off the vehicle ? If it shows correct operation off the vehicle, with a meter, then the causes of "no horn" could be numerous.
Give us a bit more info.
Like, if you manually earth the wire in the centre of the steering wheel, the one
to the horn switch (this is how it works) does the horn sound ?