Electrical fires are like airplane crashes, there is almost always more than one fatal flaw.
1. There is a rumor that the hot side of the ignition switch can overheat on 69 mustangs, the re-pop harness supposedly addressed this issue.
2. There is also the rumor of aftermarket alternators, if they short out, will burn the electrical harness.
Here is discussion on the horn switch subject.
http://www.1969stang.com/mustang/forum/showthread.php?t=6796The horn switch alone cannot cause a short circuit. It can fail either open so that the horn will not work, or closed so that the horn will stay on.
If the horn stayed on, as in the case of your friend, then the continuous current draw could exploit a weak connector which could heat up and ignite something in the vicinity.
Since horn supply voltage flows through the turn signal switch, a fire could be caused by an off shore turn signal switch and/or offshore horns.
The turn signal assembly is primarily made of plastic. Theoretically, if the horns are stuck on due to a faulty horn switch, and a higher than designed current load existed to the horns, a metal component in the plastic turn signal assembly could get hot enough to ignite the plastic. Perhaps the original Ford plastic turn signal switch was of a robust construction and design which could handle a extended period of current draw, whereas the offshore plastic turn signal switch cannot. This scenario seems more likely.
The poster on the above link "69 Stang" mentioned horn trouble and a smoke from his steering wheel. Where's there's smoke, there's fire.
Just a guess.
Thanks for the info Jeff.