Blown 35A fuse, dead electrics and a small fire

That area that was burned under the loom-was the brown wire laying on the outside of the loom directly over the burned area??

Also,  check the entire length of the white wire from the burned fuse all the way to the ignition switch.  Then follow along the brown wire after the ignition switch.  Those wires possibly got red hot when you bypassed the fuse. Their insulation may be toast. Flex the wires to see if the insulation is pliable without cracking.

Look under the fuel tank for arching marks.  The brown wire may have gotten pinched on the fuel tank mounts at the front of the tank.

That brown wire coming off the reg/rec may be a sense wire that detects the system voltage.


check this area as well(green circle)
The brown wire could have been cut by this mount.
If the insulation was cut, the brown wire would short to ground, get red hot and blow the fuse on the white wire.

I'm still scratching my head as to why the 35A fuse blew (I acknowledge it should have been 20A. I wasn't aware one of the previous owners had chosen to use 35A until this incident)? That fuse connects to the rectifier/regulator, starter relay, the ignition switch, and the battery. Would a peripheral device, such as the horn or the turn signal controls, blow this fuse if faulty? My head is perhaps in the space of domestic wiring, where there are circuits, each with a fuse and I'm thinking, the horn isn't on the 20A fuse, However, my thinking may be faulty.
Your 35 amp fuse possibly blew because if that brown wire shorted to ground, you would be pulling well over 35amps through that white wire-ignition switch-brown horn wire-to the shorting point. Your brown wire under the tank would become the fusible link when you used the aluminum foil. If you look inside a toaster when it's fully on, That's what that brown wire under the tank looked like when you bypassed the fuse.
Fuses are there to protect the wire.

Can you cut off the red heat shrink from that brown wire connection and post the photo of what is underneath that?


 

The brown wire is hot (+12 volts) when ignition switch is on.
The brown wire came in contact with ground melting brown wire.
Likely candidates are horn, front brake switch, rear brake switch and others.
Can you determine where the brown wire is most burnt ?
This would be a clue where the short occurred.

Would a peripheral device, such as the horn or the turn signal controls, blow this fuse if faulty?

Yes, the internal horn wires can decay resulting in a connection between brown wire and ground.

 

I'll carry out your suggestions over the weekend.
Meanwhile, I have a theory about the root cause.
I changed the broken odometer cable recently, Doing that involved cutting a couple of cable ties to remove it.
As part of this current problem, I prepared to remove the horn, to measure its resistance and check for any damage. As I removed the two spade-connectors I noticed the metal-shielded clutch cable wedged between the pair of horn connector points and the horn itself. See the attached picture.
My suspicion is that in removing the cable ties, I released the (unnoticed) clutch cable from a fixed point and it was freer to flap around than before. On a right turn, which was the first after 2 left turns, it was caught by the horn and settled into where you see it in the picture. My guess is there was some metal exposed between the shielded live spade connector and the pin on the horn, and the clutch cable made contact. This gave the current for the horn a route to earth, the current surged and the fuse blew.

Does this theory hold water? Would that brown horn wire be live, or should it be protected by the horn rocker switch, in which case this was an unfortunate series of events where the horn switch was faulty, i.e. allowing current to the horn, AND the accidental positioning of the clutch cable on the horn?

That definitely could be it.
The terminals are really close to that clutch cable. There may be evidence of arcing on the clutch cable. Possibly inside the blue circle below. In fact, the positive terminal of the horn my have suffered heat damage unless it was already bent upwards.

Brown wire is live when the bike is on.
The switched wire for the horn is ground.

 

I've replaced the burnt and damaged sections of wires, and replaced the 20A fuse holder with an inline 20A auto fuse and holder. 
I couldn't check the full length of the white wire from the fuse to the ignition switch because I didn't fully strip the wiring loom. I checked what I could. It is conducting end to end ok.
The electrics are now good when I switch on the ignition  . Everything works bar two consumers - rear nearside indicator (blown bulb - I'll replace that) and the horn.
I'm convinced the horn's live connection is good. Before I secured the heat shrink, I checked the wire from my soldered joint at the split from the feed brown wire to it's end. I also tested the horn across the battery and it works. My guess then is it is the return black wire. I cannot see where it terminates in the switch gear, unless it is the one held by the philips head screw, but that is by the indicator switch. See the attached picture. There is no conductivity from the horn-end of the black return wire to that black wire.

I've also attached a picture of the spade connector on the live horn wire that melted to connect to the clutch cable.

Next step: read the "Open circuit" section of the guide kindly shared by Wookie58.

wrote:

I've replaced the burnt and damaged sections of wires, and replaced the 20A fuse holder with an inline 20A auto fuse and holder. 
I couldn't check the full length of the white wire from the fuse to the ignition switch because I didn't fully strip the wiring loom. I checked what I could. It is conducting end to end ok.
The electrics are now good when I switch on the ignition 

. Everything works bar two consumers - rear nearside indicator (blown bulb - I'll replace that) and the horn.
I'm convinced the horn's live connection is good. Before I secured the heat shrink, I checked the wire from my soldered joint at the split from the feed brown wire to it's end. I also tested the horn across the battery and it works. My guess then is it is the return black wire. I cannot see where it terminates in the switch gear, unless it is the one held by the philips head screw, but that is by the indicator switch. See the attached picture. There is no conductivity from the horn-end of the black return wire to that black wire.

I've also attached a picture of the spade connector on the live horn wire that melted to connect to the clutch cable.

Next step: read the "Open circuit" section of the guide kindly shared by Wookie58.

This is where the horn black ends up. The ground is switched so the black from the horn goes through the switch to this point then grounds through the handlebars

 

You won't have continuity with that screw until you push the horn button.

Look at the wires in the circle.  Those may be your horn wires.  One will go to the horn.
The other should go to ground which is possibly the shell of that switch gear.
If the shell isn't grounded right now,  then it may need to receive its ground through the handlebars and it won't work until it is mounted to the handle bars.
I think on my bike I just ran a separate ground wire to the shell because my handbars were aftermarket coated.
Take a voltage reading.
One probe on the positive terminal of the battery and the other probe on the shell of the switch gear.  Then move that shell probe to the handlebars.  You should see battery voltage at one of those points.
If you see it at the handlebars only,  then the shell needs to be mounted securely to the bars for the horn to work.
If you don't see voltage at either point then you need to run a ground wire to that screw terminal on the switch gear shell.

 

All is now working. I ended up removing the horn/flasher rocker switch and giving it a good soak in WD40. After reassembly, the horn and flasher worked perfectly. 

it turns out the return black wire from the horn connects to the switch, not earth. See picture. 

thank you Wookie58 and F64, and everybody else that took time to contribute and respond. I doubt I would have fixed it without you.

post script: the dipped headlamp is now glowing dimly and the main beam isn’t coming on. Indicators, brake light and dashboard all nice and bright. Sigh. If I can’t fix this there might be another new forum from me. 

Be lucky, let us know if you are still struggling

Do a voltage drop test on the headlamp.

Get your meter.
key on
engine running.

black probe on the negative battery terminal
red probe on the positive battery terminal.
what is your voltage to the tenth(ex 12.4v)

move your red probe to the back of the headlight.
red/yellow should be close to battery voltage
black/yellow should be close to zero as possible.

switch to high beam and take the measurements again on the black/red wire.
This wire should be close to battery voltage.
black/yellow as close to 0.0v as possible.
what are your voltages?

turn off bike