Hi,
A 1.5 F cap is a huge one. Any voltage differental between it and the battery will more than likely draw an arc (spark).This should be normal. Also the input to your amp will have some heavy caps on it as well.
As a test, disconect the line to the amp and open the positive line to the cap. Touch the wire and see if there is any spark. If there is no load, there should be none. As a quick check, put a lamp in series with the battery lead. It should stay dark. If there is a load of some kind, the bulb will glow. Reconnect the cap, the lamp should flair then get dim. That is the current surge into a discharged cap, as the difference in voltage from the battery to the cap closes to zero, the brightness of the lamp will gradually dim. If the cap is what we call "leaky" that is a soft short from pos terminal to net, the the bulb might glow softly. You may have to do some voltage tests to be real sure. A leaky cap can dump the charge in your battery. Sometimes leaky is temp related, so in the summer it's ok, and the winter it draws or the reverse. There will always be some leakage in big caps, so it's a judgment call. If it draws more than the car clock in standby, chuck it.
There should be no leakage from the insides of the cap. The gooey stuff you discribe is more than likely it's internal dielectric. If it's a modern BCB free type of part it should not be toxic. Examine the top of the cap, between the two terminals there should be some kind of small hole and a rupture disk inside. That disk will burst if the internal temps/pressure in the cap exceed some pre set level.
What will cause a cap to pop?
Hooked up backwards is the most commen item. Second if you had an alternator puting out more AC than DC. (shorted diodes) The cap will be conducting and discharging at the alternator frequency. A 1.5F cap will pull a large amount of current and heat up to the burst point.
Incorrect voltage. If you have a 10 volt cap, and run 15 volts into it. Sooner or later it will break down and blow it's guts out.
Some can't take too much heat. If they cook from external heat that too will raise the internal temperature/pressure then pop, you have a mess.
If it's dented or over compresed by a clamp of some kind.
Lastly some caps just suck or are old stock repacked with fancy new overwraps on them. Caps are an electro chemical device and have a service life, like a battery.
The real question is why is the battery terminal burned. Since you did not talk about any failing in your amp, my best guess is a lousy crimp on the connector. Poor crimps are resistive, and will heat up under load. As the crimp join heats, it melts the insulation around the crimp.
My advice is to cut the wire back and see if it looks burned about six inches away. If not, replace the conector and solder it in this time. Apply a good wrap of tape to keep water and under hood junk out of it.
If the wire shows heat stress, go back about two inches at a time. If it looks like an old penney (oxidixed) you may have to replace the wire with something fresh. Oxygen is not a friend to electronics and wires. Use the old cable as a pull for the new one. Solder and tape as before.
Im guessng that the jbl number is a total watts delivered kind of value. 1200 watts in a car is large enough to get my interest. I used to fix audio amps used in vibration work. I repaired 80,000 watt units, tube and solid state. That kind of power requires respect and no short cuts.
One of the field coil taps (electrodynamic transducer aka speaker) ran at 275 amps at 90 volts. Roughly 25k watts of DC energy to make the magnetic field for these shakers. At that current level we had to fix some of the crimp on connectors that fed the power. Once they start to fail, they tended to keep going. It's a problem that will not go away or get better.
Find a good tech type to help you out. If you know any ham radio types that build their own gear, they should have a clue as to solving your issue.
Much luck
Jack Crow in VA.
I ve checked the cap and it is ok gooey stuff outta the cap. so it seems ok