You are talking about a hand brake cable that is pulled via the handle and it links mechanically to calipers on the rear wheels, right?
If so, what does it have to do with electrical systems at all? How can you possibly have electric current flowing thru this cable to a point of burning?
If this is in fact draining 12V battery, it would need a direct electrical contact from the battery positive, bypassing any fuses, to touch the brake cable at some point. I can't even imagine how such thing can be possible.
BTW, if you battery got drained to 2V it probably won't live much longer, so once you resolve this issue, you might want to get a new 12V battery so you don't get stranded on the road.
If so, what does it have to do with electrical systems at all? How can you possibly have electric current flowing thru this cable to a point of burning?
If this is in fact draining 12V battery, it would need a direct electrical contact from the battery positive, bypassing any fuses, to touch the brake cable at some point. I can't even imagine how such thing can be possible.
BTW, if you battery got drained to 2V it probably won't live much longer, so once you resolve this issue, you might want to get a new 12V battery so you don't get stranded on the road.