I had a close call with my Golde Top resulting in an engine compartment fire when I first bought it years ago. Luckily, it happened in my presence and I was able to extinguish the fire before any serious damage resulted.
I had remove the horns in order to clean them. I then reinstalled them. A few minutes later, I saw smoke and fire in the engine compartment. It was near the horns and I realized it was electrical. I disconnected the battery and doused the fire with water.
There is very little clearance between the horns on a 1960 and a large bundle of wires that runs right beside them. When I reinstalled the horns, one them was compressing the wiring.
I had to rebuild that section of cable. It was a long job as there are many wires in that cable.
I think I posted this years ago on the newslist, but it bears repeating. The wiring next to horns on a 1960 should be checked periodically. The horns can rub through there. Some of those wires always have current, so a short can occur even when the car is off.
Kevin is right. It is a good idea to disconnect the battery when you park your car. You have nothing to lose. There is no computer to lose its setting, plus it is small theft deterrent.
1959 Hard Top
1960 Golde Top