the earth for the horn is thru the horn switch. the horns get ignition live feed at all times. if the relay clicks, the wiring is fine. what it could be is horns are old and worn and need more power to sound than is getting thru the old wiring. put 12v to the +ve side of the horn from the battery, but leave the -ve wire connected. if they wortk, you know the issue is from the live side. if not, swap trhe procedure, use std live wire and earth the horn to the battery. if that works, you know the issue is with the live wire.
try swapping the 53 horn relay with another one to start with. if that doesnt help make a horn relay loom same as you would make a headlight relay loom, except trigger the relay weith the earth wire from the old horn loom instead.
horn need a lot of power to work, i fitted a gti horn to my driver and it couldnt run it with the engine off, you had to switch the engine on to give it enough power. i hadn't fitted a relay at the time which was the reason why