you can try to interface at the horn like howie said or you can go straight to the source and keep everything inside.
the factory horn wire on your FJ is GREEN/ red, meaning green with a red stripe. its polarity is negative, meaning when you press the horn this wire will show ground on a voltage meter. the wire is running along the steering column in the main harness and its probably really small gauge.
you should take the plastic panels off of the steering column to get to this wire. once you think you have found it you need to test it with a digital multi meter, not a test light or anything else because these wires will be ran with data wires and airbag wires. if you dont have a multi meter dont try this until you have one. if you do have one then the wire will show around +12v at rest and when you honk the horn it will change to ground and show no voltage, when you release the horn it will go back to showing +12v.
once you are 100% sure its the right wire, you need to cut it and probably extend both sides so they will reach where you will mount the small SPDT automotive relay. when you cut the wire you will have two sides, the side that runs toward the steering wheel will be connected to the relay terminal marked "30". the other side you are left with will be connected to terminal "87a".
when you are done with that part, honk the horn to make sure it still blows.
terminal "85" should be hooked to an accessory wire. the accessory wire should be WHITE/ green at the ignition switch which is where you put the key. this wire will only show +12v with the key in the run position and will also turn off while you crank the starter. when you find this wire dont assume its the right wire, test it and make sure.
terminal "86" of the relay needs to be screwed to ground and ran through whatever you will be using as your on/off switch.
the last terminal on the relay should be "87". this will go to the negative side of the air horn (not the compressor). the air horn should have two wires on it and they might both be the same color. this means that they arent polarized and it doesnt matter which one is + or -. the wire that you have left at the air horn after you connect one side to the relay's 87 can either go to 12v accessory or 12v constant. which one you hook it to depends on if you want the horn to be able to blow when the car is turned off.
lastly, the compressor will have two wires. the ground (usually black) will go straight to ground. the red NEEDS to go to a high current accessory, dont hook it straight to the battery because if there are any leaks at all it will just sit there and run all the time until the battery is dead. to do this you will have to run it through another relay because the accessory circuit probably wont have enough to power it directly nor would i chance it blowing a fuse in the car. use
THIS DIAGRAM to wire that relay. the "remote input" will go to the car's accessory and the "fans" will be your compressor +12v feed. run the +12v from the relay straight to the battery using some 14 gauge wire or thicker and you must fuse this wire close to the battery. look at the spec sheet for the compressor and it will tell you how much current it should draw and use a fuse that is as close as possible to what it is rated for.
hope that wasnt too confusing, its not as hard as it might sound but i also didnt cut any corners either.