You should have 4 cables that hook up to the solenoid. Once the solenoid is installed the positive battery cable goes to the left side. The big stud. If you're looking straight at it. If you are standing over it it will be the front side of car, or your right side. There should be another cable that runs opposite of that side to the starter. There is only one place on the starter for this to hook up too. Make sure there is a good connection there. The 2 smaller cables are for ignition and start. The smaller hookup on the left side (same side as battery positive) should be your S, the other I.
That solenoid is a momentary solenoid. If it is used constantly it will get hot.
I am not completely sure on why you battery in your Mustang would be smoking only when connected to the starter. I would take into a shop and have them look at it.
The power top on a 66 Mustang convertible doesn't have a fuse. There is a circuit breaker attached to the hot side of the starter solenoid with a wire that goes to the switch on the dash, and the wiring goes from the switch to the pump/motor assembly that is mounted between the trunk and the rear seat back. No fuse.
Lower rear passenger side of engine, bolted to the transmission bell housing.
It is located on the blocked above the starter. You must remove the starter to see it.
There will be a small wire running to the solenoid and then of course, the battery wire. Using a screwdriver you can "connect" the two. Not recommended, but it does work.
The power top doesn't have a fuse. It has a circuit breaker attached to the hot side of the starter solenoid with a wire that goes to the switch. The wiring goes from the switch to the pump/motor assembly located between the trunk and the back of the rear seat.
It's on top of the transmission case. To get to it, go under the car on the passenger side, near the right rear wheel. Look on top of the transmission case at the widest end and you'll see a large cylindrical object - that's the starter. There will be a smaller cylinder on top of the starter - that is the solenoid. If you need to replace the starter, it is recommended that you replace both the starter and solenoid.
ford mustang 1966
The top speed for the 1966 Ford Mustang is around 150 to 170
http://auto.howstuffworks.com/1965-1966-ford-mustang-specifications.htm
You'll find the starter where the trans meets the engine on the passengers side of the engine. Remove the electrical connectoions after disconnecting the battery, remove the 2 securing bolts on the starter and pull it away from the engine. Install is reverse of removal.