Not disputing what you say re fuses, but to put it at it's most simplistic, if wires are burning and the fuse ain't blowing, the rating is too high!
From what Bob actually said originally, the seat was shorting the negative battery terminal to earth, therefore the fuse would not have been protecting the positive wire, which was the one that burnt out.
Also a 35A blow fuse shouldn't result any damage being done to the wiring if it a dead short did occur in the system (I certainly know this from experience!) although I do agree it makes more sense to fit fuses to protect individual circuits.
Adding up all the load on a TR6C's system, and it's nowhere near even the quoted 17.5A,
A typical late 60's Triumph would have:
50W Headlamp main beam
6W Pilot/Park (stays on with headlamp as far as I know?)
5W Tail light
21W Brake light
3W Speedo light
3W Tacho light (if fitted?)
2W Ignition warning light
2W High beam warning light
25W+ (approx) Ignition system
60W+? Horn
_________
= 177W
Theoretically, all those circuits could be in operation simultaneously, so would draw around 14.7A of current 177W/12V = 14.75A).
And with the normal extra (20%?) safety margin added it would become 17.7A continuous.
So a 17A continuous (35A blow) fuse would be about the right amp rating I think?