As a preliminary to electrical diagnosis, always take a look at the fuses. First remove the horn's electrical connection. To check horn, connect battery voltage to the horn terminal with the jumper wire, if the horn does not beep replaced with the new one. If, however, it does sound check for voltage at the terminal whenever the horn button is pressed. If you get a voltage at the terminal then look for a bad ground in the electrical connection of the horn. But if you find no voltage at the horn, check the 
Relay. If the relay is working then measure voltage in the power and control circuits of the relay, if nothing is being supplied to any of these circuits then, check the wiring between the relay and the fuse board. If both relay circuits are getting voltage, push down the horn button and probe the circuit from the relay to the horn button for ohm readings to ground. If there is no continuity then go for an open circuit; if you do not get an open circuit then replace the horn button. If there is continuity through the horn button to ground, make test for open or short circuit from the relay to the horn. For replacement, note that there are two horns: on 2004 and earlier Highlander and 2003 and earlier Lexus models one is located in front of the condenser and the other below and in front of the engine compartment fuse and relay box while on 2005 and later Highlander and 2004 and later Lexus models both horns are located in front of the condenser. For the latter models, unbolt the radiator support trim panel and the panel and the grille from the radiator support. Remove the horns; on the cover beneath and forward of the fuse and relay box, you are required to unplug the electrical connector and then remove the mounting bracket bolt. To release the horn(s) situated in front of the condenser, the electrical connector should be disconnected the mounting bracket bolt, and also should be removed. Last of all, you need to unscrew the bracket bolt, and basically going about the process in reverse is installation.