G'day, Warbucks
To confirm the condition of your horn, remove it from the bike and connect the horn's terminals to a known-good battery. If it honks, you'll need to trace the wires to find the fault.
One horn wire is a ground wire. You might jumper the brown wire (earth on BMWs) terminal somewhere else on the chassis and hit the horn button. If it honks, you have a ground fault.
The horn button could still be the culprit so a continuity check would be helpful.
There's always the possibility that an insect, such as a wasp, has built a mud nest up in the horn and has rendered it inoperative.
Take you old flasher relay to the auto parts dealer. Match up the pins and their terminal numbers with a new relay. The relay is a common unit used on VWs and other vehicles. They are very economical. I wouldn't waste time nor money trying to source a new relay from a Beemer dealer.
After converting one of my R65s to smaller, LED turn signals, I spent $5.00 on a new relay that is designed for LED operations. Plug n' play.
You may also consider eliminating the old-school Euro ceramic and cheese string fuses. Newer 'blade' mini-fuses are easily tapped into the existing wires at the terminal box. BTW, toss the plastic box, too. Auto parts stores sell small, rubber, weatherproof fuse holders, too.