I would open the headlight shell and let the headlight and guts hang out. Inspect all the connections inside the shell or switch connections. Make sure no wires are bare or in contact with the shell. Try the key and switch again with a new fuse in the holder, while observing the wiring in the shell. If there's no visible or audible arcing to ground and the fuse blows again, I would move to look at the switch blocks, and particularly the horn switch...
Clean up all the ragged connections. I really like to use heat shrink coverings on connections and dielectric grease. It gives that extra level of corrosion and shorting protection. Make sure the headlight isn't pressing any wires up against the 3 position switch when it's reassembled back to the shell.
Undo the switch blocks and let them hang so you can observe their guts. Turn the key on again. Observe the switch block wires for some sort of arcing, then check to see if the new fuse blew again during that test. If it didn't blow, jiggle the switch block and see if you can get it to blow the fuse. Clean the connections, make sure there are no ragged wires and reassemble. Be aware that bolting the switch block back up can pinch wires.
Personally, I don't like those barrel fuse connectors. I think they corrode and cause intermittent electrical flow. That sort of flow acts like a spot welder and can burn up fuses just because their connection is poor. I spliced a blade style fuse in it's place and run a 20 amp blade style fuse in it and have no issues with that set up
Beyond those suggestions, electricity is logical. Try looking at the schematic, and disconnect a circuit at a time to see if you can isolate the problem... If your horn is acting weird, I'd disconnect that first... but NOT at the horn itself because that still leaves the switch with power in the circuitry...
Also, the crapiest thing on a norton is the chromed plastic directionals. Their grounds are screwed into the plastic/chrome base of the fixture. I always run a ground wire back through the stalk of the directional to the frame to give them a better connection. This way they either work or they blow the fuse. The poor grounding can cause intermittent problems which (as you are finding out) are the hardest to track down. Corroded bulbs in their sockets can do weird things too, check them all, clean them up, dielectric grease them, and reinstall.