1999 Lincoln Town Car horn

I can suggest things to check, but, you have to do the testing? Did you check for voltage at the fuse with key on?
If you use a jumper wire between terminals 30 and 87 at the relay, the horn should sound, does it? If it does, the problem is on the control side of relay, 86 is voltage, 85 is ground. For testing, you could use a redundant ground coming off terminal 85 wiring, if you can get at it? If the horn sounds, the problem is either the wiring circuit or one of those modules in the wiring diagram.
Can you check for applicable trouble codes, to see if it might point to one of those modules as a problem?